## 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) 812
(ii) 972
(iii) 1052
(iv) 9972
(v) 6.12
(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) = x2 + (a + b)x + ab, find the following products:
(i) (x + 7) (x + 3)
(ii) (3x + 4) (3x – 5)
(iii) (p2 + 2q) (p2 – 3q)
(iv) (abc + 3) (abc – 5)
Solution:

Question 5.
Using the identity, (x + a) (x + b) = x2 + (a + b)x + ab, evaluate the following:
(i) 203 × 204
(ii) 8.2 × 8.7
(iii) 107 × 93
Solution:

Question 6.
Using the identity a2 – b2 = (a + b) (a – b), find
(i) 532 – 472
(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) (p2 – q2r)2 + 2p2q2r
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 x2 + $$\frac{1}{x^{2}}$$ = 23, evaluate:

Solution:

Question 12.
If a + b = 9 and = 10, find the value of a2 + b2.
Solution:

Question 13.
If a – b = 6 and a2 + b2 = 42, find the value of
Solution:

Question 14.
If a2 + b2 = 41 and ab = 4, find the values of
(i) a + b
(ii) a – b
Solution: