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
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 :
b) 1 + x + x2
Solution:
Given expression 1 + x + x2
Tree Diagram :
c) y – y3
Solution:
Given expression y – y3
Tree Diagram :
d) 5xy2 + 7x2y
Solution:
Given expression 5xy2 + 7x2y
Tree Diagram :
e) -ab + 2b2 – 3a2
Solution:
Given expression -ab + 2b2 – 3a2
Tree Diagram :
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:
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:
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:
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:
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:
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
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