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