## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Check Your Progress

Question 1.

Add the following expressions:

(i) -5x^{2}y + 3xy^{2} – 7xy + 8, 12x^{2}y – 5xy^{2} + 3xy – 2

(ii) 9xy + 3yz – 5zx, 4yz + 9zx – 5y, -5xz + 2x – 5xy

Solution:

Question 2.

Subtract:

(i) 5a + 3b + 11c – 2 from 3a + 5b – 9c + 3

(ii) 10x^{2} – 8y^{2} + 5y – 3 from 8x^{2} – 5xy + 2y^{2 }+ 5x – 3y

Solution:

Question 3.

What must be added to 5x^{2} – 3x + 1 to get 3x^{3} – 7x^{2} + 8?

Solution:

Question 4.

Find the product of

(i) 3x^{2}y and -4xy^{2}

(ii) –\(\frac{4}{5}\)xy, \(\frac{5}{7}\)yz and –\(\frac{14}{9}\)zx

Solution:

Question 5.

Multiply:

(i) (3pq – 4p^{2} + 5q^{2} + 7) by -7pq

(ii) (\(\frac{3}{4}\)x^{2}y – \(\frac{4}{5}\)xy + \(\frac{5}{6}\)xy^{2}) by – 15xyz

Solution:

Question 6.

Multiply:

(i) (5x^{2} + 4x – 2) by (3 – x – 4x^{2})

(ii) (7x^{2} + 12xy – 9y^{2}) by (3x^{2} – 5xy + 3y^{2})

Solution:

Question 7.

Simplify the following expressions and evaluate them as directed:

(i) (3ab – 2a^{2} + 5b^{2}) x (2b^{2} – 5ab + 3a^{2}) + 8a^{3}b – 7b^{4} for a = 1, b = -1

(ii) (1.7x – 2.5y) (2y + 3x + 4) – 7.8x^{2} – 10y for x = 0, y = 1.

Solution:

Question 8.

Carry out the following divisions:

(i) 66pq^{2}r^{3} ÷ 11qr^{2}

(ii) (x^{3} + 2x^{2} + 3x) ÷ 2x

Solution:

Question 9.

Divide 10x^{4} – 19x^{3} + 17x^{2} + 15x – 42 by 2x^{2} – 3x + 5.

Solution:

Question 10.

Using identities, find the following products:

(i) (3x + 4y) (3x + 4y)

(ii) \(\left(\frac{5}{2} a-b\right)\left(\frac{5}{2} a-b\right)\)

(iii) (3.5m – 1.5n) (3.5m + 1.5n)

(iv) (7xy – 2)(7xy + 7)

Solution:

Question 11.

Using suitable identities, evaluate the following:

(i) 105^{2}

(ii) 97^{2}

(iii) 201 × 199

(iv) 87^{2} – 13^{2}

(v) 105 × 107

Solution:

Question 12.

Prove that following:

(i) (a + b)^{2} – (a – b)^{2} + 4ab

(ii) (2a + 3b)^{2} + (2a – 3b)^{2} = 8a^{2} + 18b^{2}

Solution:

Question 13.

If x + \(\frac{1}{x}\) = 5, evaluate

Solution:

Question 14.

If a + b = 5 and a^{2} + b^{2} = 13, find ab.

Solution: