Q1. Using the identity (a + b)2 = a2 + 2ab + b2, expand the following: (i) (7x + 4y)2 (ii) (7/5 x + 3/2 y)2 (iii) (2.5p + 1.5q)2 (iv) (3/4 s + 8t)2 (v) (x + 1/(2y))2 (vi) (1/x + 1/y)2
Answer:
(i) (7x + 4y)2 = (7x)2 + 2(7x)(4y) + (4y)2 = 49x2 + 56xy + 16y2
(ii) (7/5 x + 3/2 y)2 = (7/5 x)2 + 2(7/5 x)(3/2 y) + (3/2 y)2 = 49/25 x2 + 21/5 xy + 9/4 y2
(iii) (2.5p + 1.5q)2 = (2.5p)2 + 2(2.5p)(1.5q) + (1.5q)2 = 6.25p2 + 7.5pq + 2.25q2
(iv) (3/4 s + 8t)2 = (3/4 s)2 + 2(3/4 s)(8t) + (8t)2 = 9/16 s2 + 12st + 64t2
(v) (x + 1/(2y))2 = x2 + 2(x)(1/(2y)) + (1/(2y))2 = x2 + x/y + 1/(4y2)
(vi) (1/x + 1/y)2 = (1/x)2 + 2(1/x)(1/y) + (1/y)2 = 1/x2 + 2/(xy) + 1/y2
Q2. Using the same identity, find the values of the following: (i) (64)2 (ii) (105)2 (iii) (205)2
Answer:
(i) 642 = (60 + 4)2 = 602 + 2(60)(4) + 42 = 3600 + 480 + 16 = 4096
(ii) 1052 = (100 + 5)2 = 1002 + 2(100)(5) + 52 = 10000 + 1000 + 25 = 11025
(iii) 2052 = (200 + 5)2 = 2002 + 2(200)(5) + 52 = 40000 + 2000 + 25 = 42025