## ML Aggarwal Class 7 Solutions for ICSE Maths Chapter 8 Algebraic Expressions Ex 8.2

Question 1.
(i) 7x, -3x
(ii) 6x, -11x
(iii) 5x2, -9x2
(iv) 3ab2, -5ab2
(v) $$\frac { 1 }{ 2 }$$ pq, $$\frac { -1 }{ 3 }$$ pq
(vi) 5x3y, $$\frac { -2 }{ 3 }$$ x3y
Solution:
(i) 7x + (-3x) = 7x – 3x = 4x
(ii) 6x + (-11x) = 6x – 11x = -5x
(iii) 5x2 + (-9x2) = 5x2 – 9x2 = -4x2
(iv) 3ab2 + (-5ab2) = 3ab2 – 5ab2 = -2ab2

Question 2.
(i) 3x, -5x, 7x
(ii) 7xy, 2xy, -8xy
(iii) -2abc, 3abc, abc
(iv) 3mn, -5mn, 8mn, -4mn
(v) 2x3, 3x3, -4x3, -5x3
Solution:
(i) 3x, -5x, 7x
= 3x – 5x + 7x
= (3 – 5 + 7)x
= (10 – 5)x
= 5x
(ii) 7xy, 2xy, -8xy
= 7xy + 2xy – 8xy
= (7 + 2 – 8)xy
= (9 – 8)xy
= xy
(iii) -2abc, 3abc, abc
= -2abc + 3abc + abc
= (-2 + 3 + 1 ) abc
= (4 – 2) abc
= 2abc
(iv) 3mn, -5mn, 8mn, -4mn
= 3mn – 5mn + 8mn – 4mn
= (3 – 5 + 8 – 4) mn
= (11 – 9) mn
= 2mn
(v) 2x3, 3x3, -4x3, -5x3
= 2x3 + 3x3 – 4x3 – 5x3
= (2 + 3 – 4 – 5) x3
= (5 – 9) x3
= -4x3

Question 3.
Simplify the following combining like terms:
(i) 21b – 32 + 7b – 20b
(ii) 12m2 – 9m + 5m – 4m2 – 7m + 10
(iii) -z2 + 13z2 – 5z + 7z2 – 15z
(iv) 5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2
(v) p – (p – q) – (q – p) – q
(vi) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
(vii) (3y2 + 5y – 4) – (8y – y2 – 4)
Solution:
(i) 21b – 32 + 7b – 20b
= 21b + 7b – 20b – 32
= (21 + 7 – 20)b – 32
= (28 – 20)b – 32
= 8b – 32
(ii) 12m2 – 9m + 5m – 4m2 – 7m + 10
= 12m2 – 4m2 – 9m + 5m – 7m + 10
= (12 – 4)m2 – (9 – 5 + 7)m + 10
= 18m2 – 11m + 10
(iii) -z2 + 13z2 – 5z + 7z3 – 15z
= 7z3 – z2 + 13z2 – 5z – 15z
= 7z3 + 12z2 – 20z
(iv) 5x2y – 5x2 + 3yx2 – 3y2 + x2 – y2 + 8xy2 – 3y2
= 5x2y + 3x2y + 8xy2 – 5x2 + x2 – 3y2 – y2 – 3y2
= (5 + 3) x2y – (5 – 1) x2 – (3 + 1 + 3) y2 + 8xy2
= 8x2y – 4x2 – 7y2 + 8xy2
= 8x2y + 8xy2 – 4x2 – 7y2
(v) p – (p – q) – (q – p) – q
= p – p + q – q + p – q
= p – p + p + q – q – q
= p – q
(vi) 3a – 2b – ab – (a – b + ab) + 3ab + b – a
= 3a – 2b – ab – a + b – ab + 3ab + b – a
= 3a – a – a – 2b + b + b – ab + 3ab
= 3a – 2a – 2b + 2b – ab + 3ab
= a + ab
(vii) (3y2 + 5y – 4) – (8y – y2 – 4)
= 3y2 + 5y – 4 – 8y + y2 + 4
= 3y2 + y2 + 5y – 8y + 4 – 4
= 4y2 – 3y

Question 4.
Find the sum of the following algebraic expressions:
(i) 5xy, -7xy, 3x2
(ii) 4x2y, -3xy2, -5xy2, 5x2y
(iii) -7mn + 5, 12mn + 2, 8mn – 8, -2mn – 3
(iv) a + b – 3, b – a + 3, a – b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5
(vii) 3x3 – 5x2 + 2x + 1, 3x – 2x2 – x3, 2x2 – 7x + 9
(viii) 7a2 – 5a + 2, 3a2 – 7, 2a + 9, 1 + 2a – 5a2
Solution:
(i) 5xy, -7xy, 3x2
= 5xy – 7xy + 3x2
= 3x2 – 2xy
(ii) 4x2y, -3xy2, -5xy2, 5x2y
= 4x2y + 5x2y – 3xy2 – 5xy2
= 9x2y – 8xy2
(iii) -7mn + 5, 12mn + 2, 8mn – 8, -2mn – 3

11mn – 4
(iv) a + b – 3, b – a + 3, a – b + 3

a + b + 3
(v) 14x + 10y – 12xy – 13, 18 – 7x – 10y + 8xy, 4xy

7x + 5
(vi) 5m – 7n, 3n – 4m + 2, 2m – 3mn – 5

3m – 4n – 3mn – 3
(vii) 3x3 – 5x2 + 2x + 1, 3x – 2x2 – x3, 2x2 – 7x + 9

2x3 – 5x2 – 2x + 10
(viii) 7a– 5a + 2, 3a2 – 7, 2a + 9, 1 + 2a – 5a2

Question 5.
Simplify the following:
(i) 2x2 + 3y2 – 5xy + 5x2 – y2 + 6xy – 3x2
(ii) 3xy2 – 5x2y + 7xy – 8xy2 – 4xy + 6x2y
(iii) 5x4 – 7x2 + 8x – 1 + 3x3 – 9x2 + 7 – 3x4 + 11x – 2 + 8x2
Solution:
(i) 2x2 + 3y2 – 5xy + 5x2 – y2 + 6xy – 3x2
= 2x2 + 5x2 – 3x2 + 3y2 – y2 – 5xy + 6xy
= 4x2 + 2y2 + xy
(ii) 3xy2 – 5x2y + 7xy – 8xy2 – 4xy + 6x2y
= 3xy2 – 8xy2 – 5x2y + 6x2y + 7xy – 4xy
= -5xy2 + x2y + 3xy
(iii) 5x4 – 7x2 + 8x – 1 + 3x3 – 9x2 + 7 – 3x4 + 11x – 2 + 8x2
= 5x4 – 3x4 + 3x3 – 7x2 – 9x2 + 8x2 + 8x + 11x – 1 + 7 – 2
= 2x4 + 3x3 – 8x2 + 19x + 4

Question 6.
Subtract:
(i) -5y2 from y2
(ii) -7xy from -2xy
(iii) a(b – 5) from b(5 – a)
(iv) -m2 + 5mn from 4m2 – 3mn + 8
(v) 5a2 – 7ab + 5b2 from 3ab – 2b – 2b2
(vi) 4pq – 5q2 – 3p2 from 5p2 + 3q2 – pq
(vii) 7xy + 5x2 – 7y2 + 3 from 7x2 – 8xy + 3y2 – 5
(viii) 2x4 – 7x2 + 5x + 3 from x4 – 3x3 – 2x2 + 3
Solution:
-5y2 from y2
= y2 – (-5y2)
= y2 + 5y2
= 6y2
(ii) -7xy from -2xy
= -2xy – (-7xy)
= -2xy + 7xy
= 5xy
(iii) a(b – 5) from b(5 – a)
= b( 5 – a) – a(b – 5)
= 5b – ab – ab + 5a
= 5a + 5b – 2ab
(iv) -m2 + 5mn from 4m2 – 3mn + 8
= 4m2 – 3mn + 8 – (-m2 + 5mn)
= 4m2 – 3mn + 8 + m2 – 5mn
= 5m2 – 8mn + 8
(v) 5a2 – 7ab + 5b2 from 3ab – 2a2 – 2b2
= (3ab – 2a2 – 2b2) – (5a2 – 7ab + 5b2)
= 3ab – 2a2 – 2b2 – 5a2 + 7ab – 5b2
= -7a2 – 7b2 + 10ab
= 10ab – 7a2 – 7b2
(vi) 4pq, -5q2 – 3p2 from 5p2 + 3q2 – pq
= (5p2 + 3q2 – pq) – (4pq – 5q2 – 3p2)
= 5p2 + 3q2 – pq – 4pq + 5q2 + 3p2
= 5p2 + 3p2 + 3q2 + 5q2 – pq – 4pq
= 8p2 + 8q2 – 5pq
(vii) 7xy + 5x2 – 7y2 + 3 from 7x2 – 8xy + 3y2 – 5
= (7x2 + 3y2 – 8xy – 5) – (7xy + 5x2 – 7y2 + 3)
= 7x2 + 3y2 – 8xy – 5 – 7xy – 5x2 + 7y2 – 3
= 7x2 – 5x2 + 3y2 + 7y2 – 8xy – 7xy – 5 – 3
= 2x2 + 10y2 – 15xy – 8
(viii) 2x4 – 7x2 + 5x + 3 from x4 – 3x3 – 2x2 + 3
= (x4 – 3x3 – 2x2 + 3) – (2x4 – 7x2 + 5x + 3)
= x4 – 3x3 – 2x2 + 3 – 2x4 + 7x2 – 5x – 3
= x4 – 2x4 – 3x3 – 2x2 + 7x2 – 5x + 3 – 3
= -x4 – 3x3 + 5x2 – 5x

Question 7.
Subtract p – 2q + r from the sum of 10p – r and 5p + 2q.
Solution:
Subtract p – 2q + r from the sum of 10p – r and 5p + 2q
By adding 10p – r + 5p + 2q and 5p + 2q, we get
= 10p – r + 5p + 2q
= 15p + 2q – r
Now, (15p + 2q – r) – (p – 2q + r)
= 15p + 2q – r – p + 2q – r
= 14p + 4q – 2r

Question 8.
From the sum of 4 + 3x and 5 – 4x + 2x2, subtract the sum of 3x2 – 5x and -x2 + 2x + 5.
Solution:
Sum of (4 + 3x) + (5 – 4x + 2x2)
= 4 + 3x + 5 – 4x + 2x2
= 2x2 – x + 9
and sum of 3x2 – 5x – x2 + 2x + 5
= 2x2 – 3x + 5
Now, (2x2 – x + 9) – (2x2 – 3x + 5)
= 2x2 – x + 9 – 2x2 + 3x – 5
= 2x + 4

Question 9.
What should be added to x2 – y2 + 2xy to obtain x2 + y2 + 5xy?
Solution:
Let the term added = Z term
i.e., Z term + x2 – y2 + 2xy = x2 + y2 + 5xy
Z term = (x2 + y2 + 5xy) – (x2 – y2 + 2xy)
= x2 + y2 + 5xy – x2 + y2 – 2xy
= 2y2 + 3xy
The required term is 2y2 + 3xy

Question 10.
What should be subtracted from -7mn + 2m2 + 3n2 to get m2 + 2mn + n2?
Solution:
Let the term subtracted = Z term
-7mn + 2m2 + 3n2 – Z term = m2 + 2mn + n2
Z term = (-7mn + 2mn + 3n2) – (m2 + 2mn + n2)
= (-7mn + 2m2 + 3n2) – (m2 + 2mn + n2)
= -7mn + 2m2 + 3n2 – m2 – 2mn – n2
= m2 + 2n2 – 9mn
The required term is m2 + 2n2 – 9mn

Question 11.
How much is y4 – 12y2 + y + 14 greater than 17y3 + 34y2 – 51y + 68?
Solution:
The required expression
= (y4 – 12y2 + y + 14) – (17y3 + 34y2 – 51y + 68)
= y4 – 12y2 + y + 14 – 17y3 – 34y2 + 51y – 68
= y4 – 17y3 – 46y2 + 52y – 54

Question 12.
How much does 93p2 – 55p + 4 exceed 13p3 – 5p2 + 17p – 90?
Solution:
The required expression
= (93p2 – 55p + 4) – (13p3 – 5p2 + 17p – 90)
= 93p2 – 55p + 4 – 13p3 – 5p2 – 17p + 90
= -13p3 + 98p2 – 72p + 94

Question 13.
What should be taken away from 3x2 – 4y2 + 5xy + 20 to obtain -x2 – y2 + 6xy + 20?
Solution:
The required expression
= (3x2 – 4y2 + 5xy + 20) – (-x2 – y2 + 6xy + 20)
= 3x2 – 4y2 + 5xy + 20 + x2 + y2 – 6xy – 20
= 4x2 – 3y – xy

Question 14.
From the sum of 2y2 + 3yz, -y2 – yz – z2 and yz + 2z2, subtract the sum of 3y2 – z2 and -y2 + yz + z2.
Solution:
Sum of 2y2 + 3yz, -y2 – yz – z2 and yz + 2z2
= 2y2 + 3yz – y2 – yz – z2 + yz + 2z2
= y2 + z2 + 3yz
and sum = 3y2 – z2 + (-y2 + yz + z2)
= 3y2 – z2 – y2 + yz + z2
= 2y2 + yz
Now, (y2 + z2 + 3yz) – (2y2 + yz)
= y2 + z2 + 3yz – 2y2 – yz
= -y2 + z2 + 2yz
= -y2 + 2yz + z2