Write the following cubes in expanded form:
Write the following cubes in expanded form:
(i) (2x + 1)3 (ii) (2a – 3b)3 (iii) [3/2 x + 1]3 (iv) [x - 2/3 y]3
Answer
(i) (2x + 1)3
Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)
(2x + 1)3 = (2x)3 + 13 + (3×2x×1)(2x + 1)
= 8x3 + 1 + 6x(2x + 1)
= 8x3 + 12x2 + 6x + 1
(ii) (2a – 3b)3
Using identity, (a - b)3 = a3 - b3 - 3ab(a - b)
(2a – 3b)3 = (2a)3 - (3b)3 - (3×2a×3b)(2a - 3b)
= 8a3 - 27b3 - 18ab(2a - 3b)
= 8a3 - 27b3 - 36a2b + 54ab2
(iii) [3/2 x + 1]3
Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)
[3/2 x + 1]3 = (3/2 x)3 + 13 + (3×3/2 x×1)(3/2 x + 1)
= 27/8 x3 + 1 + 9/2 x(3/2 x + 1)
= 27/8 x3 + 1 + 27/4 x2 + 9/2 x
= 27/8 x3 + 27/4 x2 + 9/2 x + 1
(iv) [x - 2/3 y]3
Using identity, (a - b)3 = a3 - b3 - 3ab(a - b)
[x - 2/3 y]3 = (x)3 - (2/3 y)3 - (3×x×2/3 y)(x - 2/3 y)
= x3 - 8/27y3 - 2xy(x - 2/3 y)
= x3 - 8/27y3 - 2x2y + 4/3xy2
