Write the following cubes in expanded form:
(i) 
(ii) 
(iii) 
(iv) 
(i) (2x + 1)3
Using identity,
(a + b)3 = a3 + b3 + 3ab (a + b)
(2x + 1)3 = (2x)3 + (1)3 + (3 * 2 * 1) (2x + 1)
= 8x3 + 1 + 6x (2x + 1)
= 8x3 + 12x2 + 6x + 1
(ii) 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) Using identity,
(a – b)3 = a3 – b3 – 3ab (a – b)
(
x + 1)3 = (
x)3 + 13 + (3 * 
x * 1) (
x + 1)
= 
x3 + 1 + 
x (
x + 1)
= 
x3 + 1 + 
x2 + 
x
= 
x3 + 
x2 + 
x + 1
(iv) Using identity,
(a – b)3 = a3 – b3 – 3ab (a – b)
(x - 
y)3 = (x)3 – (
y)3 – (3 * x * 
y) (x - 
y)
= x3 - 
y3 – 2xy (x - 
y)
= x3 - 
y3 – 2x2y + 
xy2
47