AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions

Well-designed AP 7th Class Maths Textbook Solutions Chapter 10 Algebraic Expressions Exercise 10.1 offers step-by-step explanations to help students understand problem-solving strategies.

Algebraic Expressions Class 7 Exercise 10.1 Solutions – 7th Class Maths 10.1 Exercise Solutions

Question 1.
Get the algebraic expressions in the following cases using variables, constants and arithmetic operations.
i) Subtraction of z from y.
ii) One-half of the sum of numbers x and y.
iii) The number z multiplied by itself.
iv) One-fourth of the product of numbers p and q.
v) Numbers x and y both squared and added.
vi) Number 5 added to three times the product of numbers m and n.
vii) Product of numbers y and z subtracted from 10.
viii) Sum of numbers a and b subtracted from their product.
Solution:
i) y – z

ii) Sum of number x and y = x + y
One half of x + y = \(\frac{x+y}{2}\)

iii) z × z = z2

iv) Product of number p and q = p × q = pq
One fourth of pq = \(\frac{pq}{4}\)

v) Square of number x = x2
Square of number y = y2
When x2 and y2 are added, the sum = x2 + y2

vi) Product of number m and n = m × n = mn.
Three times the product of mn = 3 mn
Number 5 is added to 3 mn, then the sum = 3 mn + 5

vii) Product of number y and z = y × z = yz
yz is subtracted from 10, then the difference = 10 – yz

viii) Sum of numbers a and b = a + b
Product of number a and b = ab
According to the problem the algebraic expression is = ab – (a + b) = ab – a – b

AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions

Question 2.
i) Identify the terms and their factors in the following expressions. Show the terms and factors by tree diagrams.
a) x – 3
Solution:
Given expression x – 3
Tree Diagram :
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 1

b) 1 + x + x2
Solution:
Given expression 1 + x + x2
Tree Diagram :
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 2

c) y – y3
Solution:
Given expression y – y3
Tree Diagram :
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 3

d) 5xy2 + 7x2y
Solution:
Given expression 5xy2 + 7x2y
Tree Diagram :
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 4

e) -ab + 2b2 – 3a2
Solution:
Given expression -ab + 2b2 – 3a2
Tree Diagram :
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 5

ii) Identify terms and factors in the expressions given below :
a) -4x +5
b) -4x + 5y
c) 5y + 3y2
d) xy + 2x2 y2
e) pq + q
f) 1.2 ab – 2.4 b + 3.6 a
g) \(\frac { 3 }{ 4 }\)x + \(\frac { 1 }{ 4 }\)
h) 0.1 p2 + 0.2 q2
Solution:
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 6

AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions

Question 3.
Identify the numerical coefficients of terms (other than constants) in the following expressions :
i) 5 – 3t2
ii) 1 + t + t2 + t3
iii) x + 2xy + 3y
iv) 100 m + 1000 n
v) -p2q2 + 7 pq
vi) 1.2 a + 0.8 b
vii) 3.14 r2
viii) 2(l +b)
ix) 0.1y + 0.01y2
Solution:
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 7

Question 4.
a) Identify terms which contain x and give the coefficient of x.
i) y2x + y
ii) 13 y2 – 8yx
iii) x + y + 2
iv) 5 + z + zx
v) 1 + x + xy
vi) 12 xy2 + 25
vii) 7x + xy2
Solution:
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 8

b) Identify terms which contain y2 and give the coefficient of y2.
i) 8 – xy2
ii) 5 y2 + 7x
iii) 2 x2 y – 15 xy2 + 7y2
Solution:
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 9

Question 5.
Classify into monomials, binomials and trinomials.
i) 4y – 7z
ii) y2
iii) x + y – xy
iv) 100
v) ab – a – b
vi) 5 – 3t
vii) 4 p2q – 4 pq2
viii) 7 mn
ix) z2 – 3z + 8
x) a2 + b2
xi) z2 + z
xii) 1 + x + x2
Solution:
AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions Img 10

Question 6.
State whether a given pair of terms is of like or unlike terms.
i) 1,100
ii) -7x, \(\frac { 5 }{ 2 }\)x
iii) -29x, -29y
iv) 14 xy, 42yx
v) 4m2 p, 4 mp2
vi) 12 xz, 12 x2z2
Solution:
i) 1, 100 are like terms
ii) -7 x, \(\frac { 5 }{ 2 }\)x are like terms
iii) -29x, -29 y are unlike terms
iv) 14 xy, 42 yx are like terms
v) 4 m2 p, 4mp2 are unlike terms
vi) 12 xz, 12 x2z2 are unlike terms

AP 7th Class Maths 10th Chapter Algebraic Expressions Exercise 10.1 Solutions

Question 7.
Identify like terms in the following :
a) -xy2, -4 yx2, 8x2, 2xy2, 7y, -11 x2, -100 x, -11 yx, 20x2 y, -6 x2, y, 2 xy, 3x
Solution:
Like terms :
-xy2, 2xy2;
-4 yx2, 20 x2y;
8 x2, -11 x2, -6 x2
7y, y
-100 x, 3x
-11yx, 2 xy

b) 10pq, 7p, 8q, – p2q2, – 7qp, -100q – 23, 12q2p2, -5 p2, 41, 2405 p, 78 qp, 13p2q, qp2, 701p2
Solution:
Like terms : 10pq, – 7qp, 78qp ;
7p, 2405p;
8q, -100q;
-p2q2, 12 q2p2
-23,41;
-5 p2, 701p2
13 p2q, q2

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