{"id":17595,"date":"2022-02-22T12:16:40","date_gmt":"2022-02-22T06:46:40","guid":{"rendered":"https:\/\/apboardsolutions.com\/?p=17595"},"modified":"2023-03-30T12:04:14","modified_gmt":"2023-03-30T06:34:14","slug":"ap-board-8th-class-maths-solutions-chapter-11-intext-questions-in-telugu","status":"publish","type":"post","link":"https:\/\/apboardsolutions.com\/ap-board-8th-class-maths-solutions-chapter-11-intext-questions-in-telugu\/","title":{"rendered":"AP Board 8th Class Maths Solutions Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 InText Questions"},"content":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions<\/a> Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 InText Questions and Answers.<\/p>\n

AP State Syllabus 8th Class Maths Solutions 11th Lesson \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 InText Questions<\/h2>\n

\u0c07\u0c35\u0c3f \u0c1a\u0c47\u0c2f\u0c02\u0c21\u0c3f<\/span><\/p>\n

1. \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c28\u0c41 \u0c24\u0c46\u0c32\u0c41\u0c2a\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 248)
\n5xy2<\/sup>, 5xy3<\/sup> – 9x, 3xy + 4y – 8, 9x2<\/sup> + 2x + pq + q
\n\u0c38\u0c3e\u0c27\u0c28.
\n5xy2<\/sup> \u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 1
\n5xy3<\/sup> – 9x \u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 2
\n3xy + 4y – 8 \u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 3
\n9x2<\/sup> + 2x + pq + q \u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f 4<\/p>\n

\"AP<\/p>\n

2. x \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c35\u0c47\u0c30\u0c4d\u0c35\u0c47\u0c30\u0c41 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 3x + 5 \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c35\u0c3f\u0c32\u0c41\u0c35 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4b\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 248)
\n\u0c38\u0c3e\u0c27\u0c28.
\n3x + 5
\n\u21d2 x = 1 \u0c05\u0c2f\u0c3f\u0c28 \u21d2 3x + 5 = 3(1) + 5 = 3 + 5 = 8
\n\u21d2 x = 2 \u0c05\u0c2f\u0c3f\u0c28 \u21d2 3(2) + 5 = 6 + 5 = 11
\n\u21d2 x = 3 \u0c05\u0c2f\u0c3f\u0c28 \u21d2 3(3) + 5 = 9 + 5 = 14<\/p>\n

3. \u0c15\u0c3f\u0c02\u0c26\u0c3f \u0c35\u0c3e\u0c1f\u0c3f\u0c32\u0c4b \u0c38\u0c1c\u0c3e\u0c24\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c28\u0c41 \u0c17\u0c41\u0c30\u0c4d\u0c24\u0c3f\u0c02\u0c1a\u0c02\u0c26\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 249)
\nax2<\/sup>y, 2x, 5y2<\/sup>, – 9x2<\/sup>, – 6x, 7xy, 18y2<\/sup>.
\n\u0c38\u0c3e\u0c27\u0c28.
\nax2<\/sup>y, 2x, 5y2<\/sup>, – 9x2<\/sup>, – 6x, 7xy, 18y2<\/sup>.
\n\u0c38\u0c1c\u0c3e\u0c24\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c41 : (2x, – 6x), (5y2<\/sup>, 18y2<\/sup>)<\/p>\n

4. 5pq2<\/sup> \u0c15\u0c41 3 \u0c38\u0c1c\u0c3e\u0c24\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c28\u0c41 \u0c24\u0c2f\u0c3e\u0c30\u0c41\u0c1a\u0c47\u0c2f\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 249)
\n\u0c38\u0c3e\u0c27\u0c28.
\n5pq2<\/sup> \u0c15\u0c41 \u0c38\u0c1c\u0c3e\u0c24\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c41 : – 3pq2<\/sup>, pq2<\/sup>, 1\/2pq2<\/sup>. \u0c2e\u0c4a||\u0c28\u0c35\u0c3f.<\/p>\n

\"AP<\/p>\n

5. A = 2y2<\/sup> + 3x – x2<\/sup> , B = 3x2<\/sup> – y2<\/sup> \u0c2e\u0c30\u0c3f\u0c2f\u0c41 C = 5x2<\/sup> – 3xy \u0c05\u0c2f\u0c3f\u0c24\u0c47 (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 150)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\nA + B
\n\u0c38\u0c3e\u0c27\u0c28.
\nA = 2y2<\/sup> + 3x – x2<\/sup>, B = 3x2<\/sup> – y2<\/sup>, C = 5x2<\/sup> – 3xy
\nA + B = (2y2<\/sup> + 3x – x2<\/sup>) + (3x2<\/sup> – y2<\/sup>)
\n= (2y2<\/sup> – y2<\/sup>) + 3x + (3x2<\/sup> – x2<\/sup>)
\n\u2234 A + B = y2<\/sup> + 3x + 2x2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\nA – B
\n\u0c38\u0c3e\u0c27\u0c28.
\nA – B = (2y2<\/sup> + 3x – x2<\/sup>) – (3x2<\/sup> – y2<\/sup>)
\n= 2y2<\/sup> + 3x – x2<\/sup> – 3x2<\/sup> + y2<\/sup>
\n\u2234 A – B = 3y2<\/sup> + 3x – 4x2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\nB + C
\n\u0c38\u0c3e\u0c27\u0c28.
\nB + C = (3x2<\/sup> – y2<\/sup>) + (5x2<\/sup> – 3xy)
\n= 3x2<\/sup> + 5x2<\/sup> – y2<\/sup> – 3xy
\n\u2234 B + C = 8x2<\/sup> – y2<\/sup> – 3xy.<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\nB – C
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (3x2<\/sup> – y2<\/sup>) – (5x2<\/sup> – 3xy)
\n= 3x2<\/sup> – y2<\/sup> – 5x2<\/sup> + 3xy
\n\u2234 B – C = – 2x2<\/sup> – y2<\/sup> + 3xy<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\nA + B + C
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (2y2<\/sup> + 3x – x2<\/sup>) + (8x2<\/sup> – y2<\/sup> – 3xy)
\n= (2y2<\/sup> – y2<\/sup>) + (8x2<\/sup> – x2<\/sup>) + 3x – 3xy
\n\u2234 A + B + C = 7x2<\/sup> + y2<\/sup> + 3x – 3xy<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\nA + B – C
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (2y2<\/sup> + 3x – x2<\/sup>) + (- 2x2<\/sup> – y2<\/sup> + 3xy)
\n= (2y2<\/sup> – y2<\/sup>) + (- x2<\/sup> – 2x2<\/sup>) + 3x + 3xy
\n\u2234 A + B – C = y2<\/sup> – 3x2<\/sup> + 3x + 3xy<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 6.
\n\u0c2a\u0c1f\u0c4d\u0c1f\u0c3f\u0c15\u0c28\u0c41 \u0c2a\u0c42\u0c30\u0c4d\u0c24\u0c3f \u0c1a\u0c47\u0c2f\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 253)
\n\u0c38\u0c3e\u0c27\u0c28.<\/p>\n\n\n\n\n
\u0c2e\u0c4a\u0c26\u0c1f\u0c3f \u0c0f\u0c15\u0c2a\u0c26\u0c3f<\/td>\n\u0c30\u0c46\u0c02\u0c21\u0c35 \u0c0f\u0c15\u0c2a\u0c26\u0c3f<\/td>\n\u0c30\u0c46\u0c02\u0c21\u0c41 \u0c0f\u0c15\u0c2a\u0c26\u0c41\u0c32 \u0c32\u0c2c\u0c4d\u0c26\u0c2e\u0c41<\/td>\n<\/tr>\n
2x
\n– 4y2<\/sup>
\n3abc
\nmn
\n– 3mq<\/td>\n		– 3y
\n– 2y
\n5bcd
\n– 4m
\n-3nq<\/td>\n		2x \u00d7 (-3y) = – 6xy
\n+ 8y3<\/sup>
\n15abc2<\/sup>c2<\/sup>d2<\/sup>
\n– 4m2<\/sup>n
\n+ 9mnq2<\/sup><\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n

7. \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c0f\u0c15 \u0c2a\u0c26\u0c41\u0c32 \u0c32\u0c2c\u0c4d\u0c27\u0c2e\u0c41 \u0c0e\u0c32\u0c4d\u0c32\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 \u0c0f\u0c15\u0c2a\u0c26\u0c3f\u0c2f\u0c47\u0c28\u0c3e? \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 253)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c05\u0c35\u0c41\u0c28\u0c41.
\n\u0c09\u0c26\u0c3e : 2xy \u00d7 5y = 10xy2<\/sup> \u0c12\u0c15 \u0c0f\u0c15\u0c2a\u0c26\u0c3f.<\/p>\n

\"AP<\/p>\n

8. (i) 3x(4ax + 8by)
\n(ii) 4a2<\/sup>b(a – 3b)
\n(iii) (p + 3q2<\/sup>)pq
\n(iv) (m3<\/sup> + n3<\/sup>) 5mn2<\/sup> \u0c32\u0c2c\u0c4d\u0c2c\u0c3e\u0c32\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 255)
\n\u0c38\u0c3e\u0c27\u0c28.
\n(i) 3x (4ax + 8by) = 3x \u00d7 4ax + 3x \u00d7 8by
\n= 12ax2<\/sup> + 24bxy
\n(ii) 4a2<\/sup>b (a – 3b) = 4a2<\/sup>b \u00d7 a – 4a2<\/sup>b \u00d7 3b
\n= 4a2<\/sup>b – 12a2<\/sup>b2<\/sup>
\n(iii) (p + 3q2<\/sup>) pq = p \u00d7 pq + 3q2<\/sup> \u00d7 pq
\n= p2<\/sup>q + 3pq3<\/sup>
\n(iv) (m3<\/sup> + n3<\/sup>) 5mn2<\/sup> = m3<\/sup> \u00d7 5mn2<\/sup> + n3<\/sup> \u00d7 5 mn2<\/sup>
\n= 5 m4<\/sup>n2<\/sup> + 5mn5<\/sup><\/p>\n

9. \u0c12\u0c15 \u0c0f\u0c15\u0c2a\u0c26\u0c3f \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c12\u0c15 \u0c2c\u0c39\u0c41\u0c2a\u0c26\u0c3f \u0c32\u0c2c\u0c4d\u0c26\u0c02\u0c32\u0c4b \u0c17\u0c30\u0c3f\u0c37\u0c4d\u0c1f\u0c02\u0c17\u0c3e \u0c0f\u0c28\u0c4d\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c41\u0c02\u0c1f\u0c3e\u0c2f\u0c3f?
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c12\u0c15 \u0c0f\u0c15\u0c2a\u0c26\u0c3f \u0c2e\u0c30\u0c3f\u0c2f\u0c41 \u0c12\u0c15 \u0c2c\u0c39\u0c41\u0c2a\u0c26\u0c41\u0c32 \u0c32\u0c2c\u0c4d\u0c26\u0c3e\u0c32\u0c32\u0c4b \u0c05\u0c28\u0c47\u0c15 \u0c2a\u0c26\u0c3e\u0c32\u0c41\u0c02\u0c1f\u0c3e\u0c2f\u0c3f.<\/p>\n

10. \u0c32\u0c2c\u0c4d\u0c2c\u0c3e\u0c32\u0c28\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 257)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(a – b) (2a + 4b)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= a(22 + 4b) – b(2a + 4b)
\n= (a \u00d7 2a + a \u00d7 4b) – (b \u00d7 2a + b \u00d7 4b)
\n= 2a2<\/sup> + 4ab – (2ab + 4b2<\/sup>)
\n= 2a2<\/sup> + 4ab – 2ab – 4b2<\/sup>
\n= 2a2<\/sup> + 2ab – 4b2<\/sup><\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(3x + 2y) (3y – 4x)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= 3x(3y – 4x) + 2y (3y – 4x)
\n= 9xy – 12x2<\/sup> + 6y2<\/sup> – 8xy
\n= xy – 12x2<\/sup> + 6y2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(2m – l)(2l – m)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= 2m (2l – m) – l(2l – m)
\n= 2m \u00d7 2l – 2m \u00d7 m – l \u00d7 2l + l \u00d7 m
\n= 4lm – 2m2<\/sup> – 2l2<\/sup> + lm
\n= 5lm – 2m2<\/sup> – 2l2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n(k + 3m) (3m – k)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= k(3m – k) + 3m (3m – k)
\n= k \u00d7 3m – k \u00d7 k + 3m \u00d7 3m – 3m \u00d7 k
\n= 3m – k2<\/sup> + 9m2<\/sup> – 3km
\n= 9m2<\/sup> – k2<\/sup><\/p>\n

11. \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26\u0c41\u0c32 \u0c32\u0c2c\u0c4d\u0c26\u0c2e\u0c41\u0c32\u0c4b \u0c0e\u0c28\u0c4d\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32\u0c41 \u0c09\u0c02\u0c21\u0c41\u0c28\u0c41 ? (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 257)
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c30\u0c46\u0c02\u0c21\u0c41 \u0c26\u0c4d\u0c35\u0c3f\u0c2a\u0c26\u0c41\u0c32 \u0c32\u0c2c\u0c4d\u0c26\u0c02\u0c32\u0c4b 4 \u0c2a\u0c26\u0c3e\u0c32\u0c41\u0c02\u0c21\u0c41\u0c28\u0c41.
\n\u0c09\u0c26\u0c3e : (a + b) (c + d) = ac + ad + bc + bd<\/p>\n

12. \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26 \u0c07\u0c35\u0c4d\u0c35\u0c2c\u0c21\u0c3f\u0c28\u0c35\u0c3f \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c05\u0c35\u0c41\u0c28\u0c4b, \u0c15\u0c3e\u0c35\u0c4b \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f. a, b, c \u0c32\u0c41 \u0c27\u0c28 \u0c2a\u0c42\u0c30\u0c4d\u0c23\u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c32\u0c41. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 260)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(a – b) \u2261 a2<\/sup> – 2ab + b2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\na = 3, b = 1
\n\u21d2 (3 – 1)2<\/sup> = (3)2<\/sup> – 2 \u00d7 3 \u00d7 1 + 1
\n\u21d2 (2)2<\/sup> = 9 – 6 + 1
\n\u2234 (i) \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c2e\u0c47.<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(a + b) (a – b) \u2261 a2<\/sup> – b2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\na = 2, b = 1
\n\u21d2 (2 + 1) (2 – 1) = (2)2<\/sup> – (1)2<\/sup>
\n\u21d2 3 \u00d7 1 = 4 – 1
\n3 = 3
\n\u2234 (ii) \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c2e\u0c47.<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(a + b + c)2<\/sup> \u2261 a2<\/sup> + b2<\/sup> + c2<\/sup> + 2ab + 2bc + 2ca
\n\u0c38\u0c3e\u0c27\u0c28.
\na = 1, b = 2, c = 0
\n\u21d2 (1 + 2 + 0)2<\/sup> = 12<\/sup> + 22<\/sup> + 02<\/sup> + 2 \u00d7 1 \u00d7 2
\n+ 2 \u00d7 2 \u00d7 0 + 2 \u00d7 0 \u00d7 1
\n\u21d2 (3)2<\/sup> = 1 + 4 + 0 + 4 + 0 + 0
\n\u21d2 9 = 1 + 4 + 4 = 9
\n\u2234 9 = 9
\n\u2234 (iii) \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c2e\u0c47.<\/p>\n

13. x = 2, a = 1 \u0c2e\u0c30\u0c3f\u0c2f\u0c41 b = 3 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 (x + a)(x + b) \u2261 x2<\/sup> + (a + b) x + ab \u0c28\u0c41 \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 260)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\nLHS = RHS \u0c05\u0c17\u0c41\u0c28\u0c47\u0c2e\u0c4b \u0c2a\u0c30\u0c3f\u0c36\u0c40\u0c32\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n(x + a) (x + b) = x2<\/sup> + (a + b) x + ab
\nx = 2, a = 1, b = 3 \u0c05\u0c2f\u0c3f\u0c28
\n\u21d2 (2 + 1) (2 + 3) = 22<\/sup> + (1 + 3) 2 + 1 \u00d7 3
\n\u21d2 3 \u00d7 5 = 4 + 4 \u00d7 2 + 3
\n\u21d2 15 = 4 + 8 + 3
\n\u2234 15 = 15 \u2234 LHS = RHS<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\nx, a \u0c2e\u0c30\u0c3f\u0c2f\u0c41 b \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c35\u0c3f\u0c35\u0c3f\u0c27 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 \u0c2a\u0c48 \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c02 \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\nx = 0, a = 1, b = 2 \u0c05\u0c2f\u0c3f\u0c28
\n\u21d2 (0 + 1) (0 + 2) = 02<\/sup> + (1 + 2) 0 + 1 \u00d7 2
\n1 \u00d7 2= 0 + 0 + 2
\n\u2234 2 = 2
\n\u2234 LHS = RHS
\n\u2234 x, a, b \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c35\u0c3f\u0c35\u0c3f\u0c27 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 LHS = RHS \u0c05\u0c17\u0c41\u0c28\u0c41.<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\na, b \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c05\u0c28\u0c4d\u0c28\u0c3f \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 LHS = RHS \u0c05\u0c17\u0c41\u0c28\u0c3e?
\n\u0c38\u0c3e\u0c27\u0c28.
\na, b \u0c2f\u0c4a\u0c15\u0c4d\u0c15 \u0c05\u0c28\u0c4d\u0c28\u0c3f \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c15\u0c41 LHS = RHS \u0c05\u0c17\u0c41\u0c28\u0c41.<\/p>\n

14. (x + p) (x + q) = x2<\/sup> + (p + q)x + pq (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 261)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n‘p’ \u0c2c\u0c26\u0c41\u0c32\u0c41\u0c17\u0c3e ‘q’ \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f. \u0c0f\u0c2e\u0c3f \u0c17\u0c2e\u0c28\u0c3f\u0c02\u0c1a\u0c3e\u0c30\u0c41 ?
\n\u0c38\u0c3e\u0c27\u0c28.
\n(x + p) (x + q) = x + (p + q) x + pq \u0c32\u0c4b
\np\u0c2c\u0c26\u0c41\u0c32\u0c41\u0c17\u0c3e ( \u0c28\u0c41 \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c17\u0c3e
\n\u21d2 (x + q) (x + q) = x2<\/sup> + (q + q) x + q \u00d7 q
\n\u21d2 (x + q) = x2<\/sup> + 24x + q2<\/sup> \u0c05\u0c17\u0c41\u0c28\u0c41.<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n‘q’ \u0c2c\u0c26\u0c41\u0c32\u0c41\u0c17\u0c3e ‘P’ \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f. \u0c0f\u0c2e\u0c3f \u0c17\u0c2e\u0c28\u0c3f\u0c02\u0c1a\u0c3e\u0c30\u0c41 ?
\n\u0c38\u0c3e\u0c27\u0c28.
\nq \u0c2c\u0c26\u0c41\u0c32\u0c41\u0c17\u0c3e p \u0c28\u0c41 \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c17\u0c3e
\n\u21d2 (x + p) (x + p) = x2<\/sup> + (p + p) x + p \u00d7 p
\n\u21d2 (x + p)2<\/sup> = x2<\/sup> + 2px + p2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n\u0c2e\u0c40\u0c30\u0c41 \u0c17\u0c2e\u0c28\u0c3f\u0c02\u0c1a\u0c3f\u0c28 \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c41 \u0c0f\u0c35\u0c3f?
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c28\u0c47\u0c28\u0c41 \u0c17\u0c2e\u0c28\u0c3f\u0c02\u0c1a\u0c3f\u0c28 \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c32\u0c41
\n(x + q)2<\/sup> = x2<\/sup> + 2qx + q2<\/sup>
\n(x + p)2<\/sup> = x2<\/sup> + 2px + p2<\/sup><\/p>\n

\"AP<\/p>\n

15. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 261)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(5m + 7n)2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(5m + 7n)2<\/sup> \u0c07\u0c26\u0c3f (a + b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(a + b)2<\/sup> = a2<\/sup> + 2ab + b2<\/sup> [a = 5m, b = 7n]
\n(5m + 7n)2<\/sup> = (5m)2<\/sup> + 2 \u00d7 5m \u00d7 7n + (7n)2<\/sup>
\n= (5m \u00d7 5m) + 70 mn + 7n \u00d7 7n
\n= 25m2<\/sup> + 70mn + 49n2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(6kl + 7mn)2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(a + b)2<\/sup> = a2<\/sup> + 2ab + b2<\/sup> \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02
\n(6kl + 7mn)2<\/sup> = (6kl)2<\/sup> + 2 \u00d7 6kl \u00d7 7mn +(7mn)2<\/sup>
\n= 36 k2<\/sup>l2<\/sup> +84 klmn + 49m2<\/sup>n2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(5a2<\/sup> + 6b2<\/sup>)
\n\u0c38\u0c3e\u0c27\u0c28.
\na = 5a2<\/sup>, b = 6b2<\/sup>
\n\u2234 (5a2<\/sup> + 6b2<\/sup>)2<\/sup> = (5a2<\/sup>)2<\/sup> + 2 5a2<\/sup> \u00d7 6b2<\/sup> + (6b2<\/sup>)2<\/sup>
\n= 5a2<\/sup> \u00d7 5a2<\/sup> + 60a2<\/sup>b2<\/sup> + 36b4<\/sup>
\n= 25a4<\/sup> + 60a2<\/sup>b2<\/sup> + 36b4<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n3022<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (300 + 2)2<\/sup>
\na = 300, b = 2
\n\u2234 (300 + 2)2<\/sup> = (300)2<\/sup> + 2 \u00d7 300 \u00d7 2 + (2)2<\/sup>
\n= 300 \u00d7 300 + 1200 + 2 \u00d7 2
\n= 90,000 + 1200 + 4
\n= 91,204<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\n8072<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (800 + 7)2<\/sup>
\na = 800, b = 7
\n(800 + 7)2<\/sup> = (800)2<\/sup> + 2 \u00d7 800 \u00d7 7 + (7)2<\/sup>
\n= 800 \u00d7 800 + 11,200 + 7 \u00d7 7
\n= 6,40,000 + 11,200 + 49
\n= 6,51,249<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\n7042<\/sup> \u0c32\u0c28\u0c41 \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (700 + 4)2<\/sup>
\na = 700, b = 4
\n\u2234 (700 + 4)2<\/sup> = (700)2<\/sup> + 2 \u00d7 700 \u00d7 4 + 42<\/sup>
\n= 700 \u00d7 700 + 5600 + 4 \u00d7 4
\n= 4,90,000 + 5600 + 16
\n= 4,95,616<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vii)
\n(a – b)2<\/sup> = a2<\/sup> – 2ab + b2<\/sup> \u0c38\u0c30\u0c4d\u0c35\u0c38\u0c2e\u0c40\u0c15\u0c30\u0c23\u0c3e\u0c28\u0c4d\u0c28\u0c3f,
\na = 3m \u0c2e\u0c30\u0c3f\u0c2f\u0c41 b = 5n \u0c06\u0c2f\u0c3f\u0c28\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 \u0c38\u0c30\u0c3f\u0c1a\u0c42\u0c21\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n(a – b)2<\/sup> = a2<\/sup> – 2ab + b2<\/sup> \u0c32\u0c4b a = 3m b = 5n\u0c28\u0c41 \u0c2a\u0c4d\u0c30\u0c24\u0c3f\u0c15\u0c4d\u0c37\u0c47\u0c2a\u0c3f\u0c02\u0c1a\u0c17\u0c3e
\nLHS = (3m – 5n)2<\/sup> = (3m)2<\/sup> – 2 \u00d7 3m \u00d7 5n + (5n)2<\/sup>
\n= 9m2<\/sup> – 30mn + 25n2<\/sup>
\nRHS = (3m)2<\/sup> – 2 \u00d7 3m \u00d7 5n + (5n)2<\/sup>
\n= 9m2<\/sup> – 30mn + 25n2<\/sup>
\n\u2234 LHS = RHS<\/p>\n

\"AP<\/p>\n

16. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 262)<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(9m – 2n)2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n(9m – 2n)2<\/sup> \u0c07\u0c21\u0c3f (a – b)2<\/sup> \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41
\n(a – b)2<\/sup> = a2<\/sup> – 2ab + b2<\/sup>
\n(9m – 2n)2<\/sup> = (9m)2<\/sup> – 2 \u00d7 9m \u00d7 2n + (2n)2<\/sup>
\n= 9m \u00d7 9m – 36mn + 2n \u00d7 2n
\n= 81m2<\/sup> – 36mn + 4n2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(6pq – 7rs)2<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\na = 6pq, b = 7rs
\n\u2234 [6pq – 7rs]2<\/sup> = (6pq)2<\/sup> – 2 \u00d7 6pq \u00d7 7rs + (7rs)2<\/sup>
\n= 6pq \u00d7 6pq – 84pqrs + 7rs \u00d7 7rs
\n= 36p2<\/sup>q2<\/sup> – 84pqrs + 49r2<\/sup>s2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(5x2<\/sup> – 6y2<\/sup>)2<\/sup> \u0c32\u0c28\u0c41 \u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c30\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (5x2<\/sup>)2<\/sup> – 2 \u00d7 5x2<\/sup> \u00d7 6y2<\/sup> + (6y2<\/sup>)2<\/sup>
\n= 5x2<\/sup> \u00d7 5x2<\/sup> – 60x2<\/sup>y2<\/sup> + 6y2<\/sup> \u00d7 6y2<\/sup>
\n= 25x4<\/sup> – 60x2<\/sup>y2<\/sup> + 36y4<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n2922<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (300 – 8)2<\/sup>
\na = 300, b= 8
\n\u2234 (300 – 8)2<\/sup> = (300)2<\/sup> – 2 \u00d7 300 \u00d7 8+ (8)2<\/sup>
\n= 300 \u00d7 300 – 4800 + 8 \u00d7 8
\n= 90,000 – 4800 + 64
\n= 90,064 – 4800 = 85,264<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\n8972<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (900 – 3)2<\/sup>
\n= (900)2<\/sup> – 2 \u00d7 900 \u00d7 3 + (3)2<\/sup>
\n= 8,10,000 – 5400 + 9
\n= 8,10,009 – 5400 = 8,04,609<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\n7942<\/sup> \u0c32 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c02\u0c21\u0c3f
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (800 – 6)2<\/sup>
\n= (800)2<\/sup> – 2 \u00d7 800 \u00d7 6 + (6)2<\/sup>
\n= 6,40,000 – 9600 + 36
\n= 6,40,036 -9600 = 6,30,436<\/p>\n

17.<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (i)
\n(6m + 7n) (6m – 7n)
\n\u0c38\u0c3e\u0c27\u0c28.
\n(6m + 7n) (6m – 7n) \u0c07\u0c21\u0c3f (a + b)(a – b) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n(a + b)(a – b) = a2<\/sup> – b2<\/sup> \u0c07\u0c15\u0c4d\u0c15\u0c21 a = 6m, b = 7m
\n(6m + 7n) (6m – 7n) = (6m)2<\/sup> – (7n)2<\/sup>
\n= 6m \u00d7 6m – 7n \u00d7 7n
\n= 36m2<\/sup> – 49n2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (ii)
\n(5a + 10b) (5a – 10b)
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (5a)2<\/sup> – (10b)2<\/sup>
\n[\u2235 (a + b) (a – b) = a2<\/sup> – b2<\/sup>]
\n= 5a \u00d7 5a – 10b \u00d7 10b
\n= 25a2<\/sup> – 100b2<\/sup><\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iii)
\n(3x2<\/sup> + 4y2<\/sup>) (3x2<\/sup> – 4y2<\/sup>) \u0c32 \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c15\u0c4d\u0c15\u0c4a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (3x2<\/sup>)2<\/sup> – (4y2<\/sup>)2<\/sup>
\n[\u2235 (a + b)(a – b) = a2<\/sup> – b2<\/sup>]
\n= 3x2<\/sup> \u00d7 3x2<\/sup> – 4y2<\/sup> \u00d7 4y2<\/sup>
\n= 9x4<\/sup> – 16y4<\/sup><\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (iv)
\n106 \u00d7 94
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (100 + 6) (100 – 6)
\n= 1002<\/sup> – 62<\/sup>
\n[\u2235 (a + b)(a – b) = a2<\/sup> – b2<\/sup>)
\n= 100 \u00d7 100 – 6 \u00d7 6
\n= 10,000 – 36 = 9,964<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (v)
\n592 \u00d7 608
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (600 – 8) (600 + 8)
\n= (600)2<\/sup> – (8)2<\/sup> [\u2235 (a + b) (a – b) = a2<\/sup> – b2<\/sup>) = 600 \u00d7 600 – 8 \u00d7 8
\n= 3,60,000 – 64
\n= 3,59,936<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vi)
\n922<\/sup> – 82<\/sup>
\n\u0c38\u0c3e\u0c27\u0c28.
\n\u0c07\u0c26\u0c3f a2<\/sup> – b2<\/sup> = (a + b)(a – b) \u0c30\u0c42\u0c2a\u0c02\u0c32\u0c4b \u0c15\u0c32\u0c26\u0c41.
\n922<\/sup> – 82<\/sup> = (92 + 8) (92 – 8)
\n= 100 \u00d7 84
\n= 8400<\/p>\n

\u0c2a\u0c4d\u0c30\u0c36\u0c4d\u0c28 (vii)
\n9842<\/sup> – 162<\/sup> \u0c32\u0c28\u0c41 \u0c38\u0c42\u0c15\u0c4d\u0c37\u0c4d\u0c2e\u0c40\u0c15\u0c30\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f.
\n\u0c38\u0c3e\u0c27\u0c28.
\n= (984 +16) (984 – 16)
\n[\u2235 a2<\/sup> – b2<\/sup> = (a + b)(a – b)]
\n= (1000) (968)
\n= 9,68,000<\/p>\n

\"AP<\/p>\n

\u0c2a\u0c4d\u0c30\u0c2f\u0c24\u0c4d\u0c28\u0c3f\u0c02\u0c1a\u0c02\u0c21\u0c3f<\/span><\/p>\n

1. \u0c35\u0c47\u0c17\u0c2e\u0c41, \u0c15\u0c3e\u0c32\u0c2e\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c02\u0c1a\u0c3f \u0c26\u0c42\u0c30\u0c2e\u0c41 \u0c32\u0c46\u0c15\u0c4d\u0c15\u0c3f\u0c02\u0c1a\u0c41 \u0c28\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41, \u0c05\u0c38\u0c32\u0c41, \u0c30\u0c47\u0c1f\u0c41 \u0c15\u0c3e\u0c32\u0c2e\u0c41 \u0c07\u0c1a\u0c4d\u0c1a\u0c3f\u0c28\u0c2a\u0c4d\u0c2a\u0c41\u0c21\u0c41 \u0c38\u0c3e\u0c2e\u0c3e\u0c28\u0c4d\u0c2f \u0c35\u0c21\u0c4d\u0c21\u0c40 \u0c32\u0c46\u0c15\u0c4d\u0c15\u0c3f\u0c02\u0c1a\u0c41\u0c1f\u0c15\u0c41 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c2e\u0c41\u0c32\u0c41 \u0c35\u0c4d\u0c30\u0c3e\u0c2f\u0c41\u0c2e\u0c41. \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c2e\u0c41\u0c32\u0c41 \u0c09\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c02\u0c1a\u0c3f \u0c35\u0c3f\u0c32\u0c41\u0c35\u0c32\u0c41 \u0c15\u0c28\u0c41\u0c17\u0c4a\u0c28\u0c41 \u0c2e\u0c30\u0c4a\u0c15 \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c38\u0c02\u0c26\u0c30\u0c4d\u0c2d\u0c2e\u0c41\u0c32\u0c41 \u0c24\u0c46\u0c32\u0c2a\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 251)
\n\u0c38\u0c3e\u0c27\u0c28.
\nd = s \u00d7 t (\u0c32\u0c47\u0c26\u0c3e) \u0c26\u0c42\u0c30\u0c02 = \u0c35\u0c47\u0c17\u0c02 \u00d7 \u0c15\u0c3e\u0c32\u0c02
\nI = \\(\\frac {PTR}{100}\\) (\u0c32\u0c47\u0c26\u0c3e)
\n\u0c38\u0c3e\u0c2e\u0c3e\u0c28\u0c4d\u0c2f \u0c35\u0c21\u0c4d\u0c21\u0c40 = \\(\\frac {\u0c05\u0c38\u0c32\u0c41 \u00d7 \u0c35\u0c21\u0c4d\u0c21\u0c40 \u0c30\u0c47\u0c1f\u0c41 \u00d7 \u0c15\u0c3e\u0c32\u0c02}{100}\\)
\n\u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c28\u0c41\u0c2a\u0c2f\u0c4b\u0c17\u0c3f\u0c02\u0c1a\u0c47 \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c38\u0c02\u0c26\u0c30\u0c4d\u0c2d\u0c3e\u0c32\u0c41 :
\n(i) \u0c24\u0c4d\u0c30\u0c3f\u0c2d\u0c41\u0c1c \u0c35\u0c48\u0c36\u0c3e\u0c32\u0c4d\u0c2f\u0c02 = \\(\\frac {1}{2}\\) \u00d7 \u0c2d\u0c42\u0c2e\u0c3f \u00d7 \u0c0e\u0c24\u0c4d\u0c24\u0c41
\n= \\(\\frac {1}{2}\\)bh
\n(ii) \u0c26\u0c40\u0c30\u0c4d\u0c18 \u0c1a\u0c24\u0c41\u0c30\u0c38\u0c4d\u0c30 \u0c1a\u0c41\u0c1f\u0c4d\u0c1f\u0c41\u0c15\u0c4a\u0c32\u0c24 = 2(\u0c2a\u0c4a\u0c21\u0c35\u0c41 + \u0c35\u0c46\u0c21\u0c32\u0c4d\u0c2a\u0c41)
\n= 2(l+ b)<\/p>\n

\u0c06\u0c32\u0c4b\u0c1a\u0c3f\u0c02\u0c1a\u0c3f, \u0c1a\u0c30\u0c4d\u0c1a\u0c3f\u0c02\u0c1a\u0c3f \u0c35\u0c4d\u0c30\u0c3e\u0c2f\u0c02\u0c21\u0c3f<\/span><\/p>\n

1. \u0c37\u0c40\u0c32\u0c3e 2pq, 4pq \u0c32 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c02 8p2<\/sup> q2<\/sup> \u0c05\u0c28\u0c3f \u0c1a\u0c46\u0c2a\u0c4d\u0c2a\u0c3f\u0c02\u0c26\u0c3f. \u0c38\u0c2e\u0c3e\u0c27\u0c3e\u0c28\u0c02 \u0c38\u0c30\u0c48\u0c02\u0c26\u0c3e ? \u0c2e\u0c40 \u0c35\u0c3f\u0c35\u0c30\u0c23 \u0c07\u0c35\u0c4d\u0c35\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 249)
\n\u0c38\u0c3e\u0c27\u0c28.
\n2pq, qpq \u0c32 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c2e\u0c41 = 2pq + 4pg = 6pq.
\n\u0c15\u0c3e\u0c28\u0c40 \u0c37\u0c40\u0c32\u0c3e \u0c38\u0c2e\u0c3e\u0c27\u0c3e\u0c28\u0c02 \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02 \u0c2a\u0c48 \u0c30\u0c46\u0c02\u0c21\u0c3f\u0c02\u0c1f\u0c3f \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c02 8p2<\/sup>q2<\/sup>
\n\u2234 8p2<\/sup>q2<\/sup> \u2260 6pq
\n\u2234 \u0c06\u0c2e\u0c46 (\u0c37\u0c40\u0c32\u0c3e) \u0c38\u0c2e\u0c3e\u0c27\u0c3e\u0c28\u0c02 \u0c38\u0c30\u0c3f\u0c2f\u0c48\u0c28\u0c26\u0c3f \u0c15\u0c3e\u0c26\u0c41.<\/p>\n

\"AP<\/p>\n

2. \u0c30\u0c46\u0c39\u0c2e\u0c3e\u0c28\u0c4d 4x \u0c28\u0c41 7y\u0c32\u0c15\u0c41 \u0c15\u0c32\u0c3f\u0c2a\u0c3f\u0c24\u0c47 11xy \u0c35\u0c38\u0c4d\u0c24\u0c41\u0c02\u0c26\u0c28\u0c4d\u0c28\u0c3e\u0c21\u0c41. \u0c2e\u0c40\u0c30\u0c41 \u0c0f\u0c15\u0c40\u0c2d\u0c35\u0c3f\u0c38\u0c4d\u0c24\u0c3e\u0c30\u0c3e ? (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 249)
\n\u0c38\u0c3e\u0c27\u0c28.
\n4x, 7y \u0c32 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c02 \u2260 4x + 7y
\n\u0c30\u0c46\u0c39\u0c2e\u0c3e\u0c28\u0c4d \u0c2a\u0c4d\u0c30\u0c15\u0c3e\u0c30\u0c02 \u0c2a\u0c48 \u0c30\u0c46\u0c02\u0c21\u0c41 \u0c2a\u0c26\u0c3e\u0c32 \u0c2e\u0c4a\u0c24\u0c4d\u0c24\u0c02 = 11xy
\n\u2234 11xy \u2260 4x + 7y
\n\u2234 \u0c28\u0c47\u0c28\u0c41 \u0c30\u0c46\u0c39\u0c2e\u0c3e\u0c28\u0c4d \u0c38\u0c2e\u0c3e\u0c27\u0c3e\u0c28\u0c02\u0c24\u0c4b \u0c0f\u0c15\u0c40\u0c2d\u0c35\u0c3f\u0c02\u0c1a\u0c28\u0c41.<\/p>\n","protected":false},"excerpt":{"rendered":"

AP SCERT 8th Class Maths Textbook Solutions Chapter 11 \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 InText Questions and Answers. AP State Syllabus 8th Class Maths Solutions 11th Lesson \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41 InText Questions \u0c07\u0c35\u0c3f \u0c1a\u0c47\u0c2f\u0c02\u0c21\u0c3f 1. \u0c15\u0c4d\u0c30\u0c3f\u0c02\u0c26\u0c3f \u0c2c\u0c40\u0c1c\u0c40\u0c2f \u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c32\u0c4b\u0c28\u0c3f \u0c2a\u0c26\u0c3e\u0c32 \u0c38\u0c02\u0c16\u0c4d\u0c2f\u0c28\u0c41 \u0c24\u0c46\u0c32\u0c41\u0c2a\u0c02\u0c21\u0c3f. (\u0c2a\u0c47\u0c1c\u0c40 \u0c28\u0c46\u0c02. 248) 5xy2, 5xy3 – 9x, 3xy + 4y – 8, 9×2 + 2x + pq + … Read more<\/a><\/p>\n","protected":false},"author":5,"featured_media":36834,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"spay_email":""},"categories":[6],"tags":[],"jetpack_featured_media_url":"https:\/\/apboardsolutions.com\/wp-content\/uploads\/2022\/02\/Chapter-11-\u0c2c\u0c40\u0c1c\u0c40\u0c2f-\u0c38\u0c2e\u0c3e\u0c38\u0c3e\u0c32\u0c41-InText-Questions.png","_links":{"self":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17595"}],"collection":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/users\/5"}],"replies":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/comments?post=17595"}],"version-history":[{"count":1,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17595\/revisions"}],"predecessor-version":[{"id":17596,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/posts\/17595\/revisions\/17596"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media\/36834"}],"wp:attachment":[{"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/media?parent=17595"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/categories?post=17595"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/apboardsolutions.com\/wp-json\/wp\/v2\/tags?post=17595"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}