## ML Aggarwal Class 8 Solutions for ICSE Maths Chapter 10 Algebraic Expressions and Identities Ex 10.5

Question 1.

Using suitable identities, find the following products:

(i) (3x + 5) (3x + 5)

(ii) (9y – 5) (9y-5)

(iii) (4x + 11y) (4x – 11y)

(iv) \(\left(\frac{3}{2} m+\frac{2}{3} n\right)\left(\frac{3}{2} m-\frac{2}{3} n\right)\)

(v) \(\left(\frac{2}{a}+\frac{5}{b}\right)\left(\frac{2}{a}+\frac{5}{b}\right)\)

(vi) \(\left(\frac{p^{2}}{2}+\frac{2}{q^{2}}\right)\left(\frac{p^{2}}{2}-\frac{2}{q^{2}}\right)\)

Solution:

Question 2.

Using the identities, evaluate the following:

(i) 81^{2}

(ii) 97^{2}

(iii) 105^{2}

(iv) 997^{2}

(v) 6.1^{2}

(vi) 496 × 504

(vii) 20.5 × 19.5

(viii) 9.62

Solution:

Question 3.

Find the following squares, using the identities:

Solution:

Question 4.

Using the identity, (x + a) (x + b) = x^{2} + (a + b)x + ab, find the following products:

(i) (x + 7) (x + 3)

(ii) (3x + 4) (3x – 5)

(iii) (p^{2} + 2q) (p^{2} – 3q)

(iv) (abc + 3) (abc – 5)

Solution:

Question 5.

Using the identity, (x + a) (x + b) = x^{2} + (a + b)x + ab, evaluate the following:

(i) 203 × 204

(ii) 8.2 × 8.7

(iii) 107 × 93

Solution:

Question 6.

Using the identity a^{2} – b^{2} = (a + b) (a – b), find

(i) 53^{2} – 47^{2}

(ii) (2.05)^{2} – (0.95)^{2}

(iii) (14.3)^{2} – (5.7)^{2}

Solution:

Question 7.

Simplify the following:

(i) (2x + 5y)^{2} + (2x – 5y)^{2}

(ii) \(\left(\frac{7}{2} a-\frac{5}{2} b\right)^{2}-\left(\frac{5}{2} a-\frac{7}{2} b\right)^{2}\)

(iii) (p^{2} – q^{2}r)^{2} + 2p^{2}q^{2}r

Solution:

Question 8.

Show that:

(i) (4x + 7y)^{2} – (4x – 7y)^{2} = 112xy

(ii) \(\left(\frac{3}{7} p-\frac{7}{6} q\right)^{2}+p q=\frac{9}{49} p^{2}+\frac{49}{36} q^{2}\)

(iii) (p – q)(p + q) + (q – r)(q + r) + (r – p) (r + p) = 0

Solution:

Question 9.

If x + \(\frac{1}{x}\) = 2, evaluate:

Solution:

Question 10.

If x = \(\frac{1}{x}\) = 7, ecaluate:

Solution:

Question 11.

If x^{2} + \(\frac{1}{x^{2}}\) = 23, evaluate:

Solution:

Question 12.

If a + b = 9 and = 10, find the value of a^{2} + b^{2}.

Solution:

Question 13.

If a – b = 6 and a^{2} + b^{2} = 42, find the value of

Solution:

Question 14.

If a^{2} + b^{2} = 41 and ab = 4, find the values of

(i) a + b

(ii) a – b

Solution: