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

Question 1.

Add:

(i) 7x, -3x

(ii) 6x, -11x

(iii) 5x^{2}, -9x^{2}

(iv) 3ab^{2}, -5ab^{2}

(v) \(\frac { 1 }{ 2 }\) pq, \(\frac { -1 }{ 3 }\) pq

(vi) 5x^{3}y, \(\frac { -2 }{ 3 }\) x^{3}y

Solution:

Question 2.

Add:

(i) 3x, -5x, 7x

(ii) 7xy, 2xy, -8xy

(iii) -2abc, 3abc, abc

(iv) 3mn, -5mn, 8mn, -4mn

(v) 2x^{3}, 3x^{3}, -4x^{3}, -5x^{3}

Solution:

Question 3.

Simplify the following combining like terms:

(i) 21b – 32 + 7b – 20b

(ii) 12m^{2} – 9m + 5m – 4m^{2} – 7m + 10

(iii) -z^{2} + 13z^{2} – 5z + 7z^{2} – 15z

(iv) 5x^{2}y – 5x^{2} + 3yx^{2} – 3y^{2} + x^{2} – y^{2} + 8xy^{2} – 3y^{2}

(v) p – (p – q) – (q – p) – q

(vi) 3a – 2b – ab – (a – b + ab) + 3ab + b – a

(vii) (3y^{2} + 5y – 4) – (8y – y^{2} – 4)

Solution:

Question 4.

Find the sum of the following algebraic expressions:

(i) 5xy, -7xy, 3x^{2}

(ii) 4x^{2}y, -3xy^{2}, -5xy^{2}, 5x^{2}y

(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) 3x^{3} – 5x^{2} + 2x + 1, 3x – 2x^{2} – x^{3}, 2x^{2} – 7x + 9

(viii) 7a^{2} – 5a + 2, 3a^{2} – 7, 2a + 9, 1 + 2a – 5a^{2}

Solution:

Question 5.

Simplify the following:

(i) 2x^{2} + 3y^{2} – 5xy + 5x^{2} – y^{2} + 6xy – 3x^{2}

(ii) 3xy^{2} – 5x^{2}y + 7xy – 8xy^{2} – 4xy + 6x^{2}y

(iii) 5x^{4} – 7x^{2} + 8x – 1 + 3x^{3} – 9x^{2} + 7 – 3x^{4} + 11x – 2 + 8x^{2}

Solution:

Question 6.

Subtract:

(i) -5y^{2} from y^{2}

(ii) -7xy from -2xy

(iii) a(b – 5) from b(5 – a)

(iv) -m^{2} + 5mn from 4m^{2} – 3mn + 8

(v) 5a^{2} – 7ab + 5b^{2} from 3ab – 2b – 2b^{2}

(vi) 4pq – 5q^{2} – 3p^{2} from 5p^{2} + 3q^{2} – pq

(vii) 7xy + 5x^{2} – 7y^{2} + 3 from 7x^{2} – 8xy + 3y^{2} – 5

(viii) 2x^{4} – 7x^{2} + 5x + 3 from x^{4} – 3x^{3} – 2x^{2} + 3

Solution:

Question 7.

Subtract p – 2q + r from the sum of 10p – r and 5p + 2q.

Solution:

Question 8.

From the sum of 4 + 3x and 5 – 4x + 2x^{2}, subtract the sum of 3x^{2} – 5x and -x^{2} + 2x + 5.

Solution:

Question 9.

What should be added to x^{2} – y^{2} + 2xy to obtain x^{2} + y^{2} + 5xy?

Solution:

Question 10.

What should be subtracted from -7mn + 2m^{2} + 3n^{2} to get m^{2} + 2mn + n^{2}?

Solution:

Question 11.

How much is y^{4} – 12y^{2} + y + 14 greater than 17y^{3} + 34y^{2} – 51y + 68?

Solution:

Question 12.

How much does 93p^{2} – 55p + 4 exceed 13p^{3} – 5p^{2} + 17p – 90?

Solution:

Question 13.

What should be taken away from 3x^{2} – 4y^{2} + 5xy + 20 to obtain -x^{2} – y^{2} + 6xy + 20?

Solution:

Question 14.

From the sum of 2y^{2} + 3yz, -y^{2} – yz – z^{2} and yz + 2z^{2}, subtract the sum of 3y^{2} – z^{2} and -y^{2} + yz + z^{2}.

Solution: