Q.6. Write the following cubes in expanded form:

(i) (2x + 1)3 (ii) (2a - 3b)3 (iii) [x + 1]3 (iv) [x - $\frac{2}{3}$ y]3

Solution:

(i) Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)

We can write,

(2x + 1)= (2x)3 + 13 + (3×2x×1)(2x + 1)

= 8x3 + 1 + 6x(2x + 1)

= 8x3 + 12x2 + 6x + 1

(ii) Using identity, (x - y)3 = x3 - y3 - 3xy(x - y)

We can write,

(2a - 3b)3 = (2a)3 - (3b)3 - (3×2a×3b)(2a - 3b)

= 8a3 - 27b3 - 18ab(2a - 3b)

= 8a3 - 27b3 - 36a2b + 54ab2

(iii) Using identity, (a + b)3 = a3 + b3 + 3ab(a + b)

We can write,

(iv) Using identity, (a - b)3 = a3 - b3 - 3ab(a -b)

We can write,