Question

Factorise (x + 4)3 - 9x - 36​

Answer 1

$3(x + 4) - 9x - 36$

$3 x + 12 - 9x - 36$

$3x - 9x + 12 - 36$

answer :

$- 6x - 24$

Answer 2

Given :-

(x + 4)³ - 9x - 36

using identity (a + b)³ = a³ + b³ + 3a²b + 3ab²

identity proof :-

(a + b)³ = (a + b) (a + b) (a + b)

= a(a + b) + b(a + b) (a + b)

= a² + ab + ab + b² (a + b)

= a³ + 2ab + b² (a + b)

= a(a² + 2ab + b²) + b(a² + 2ab + b²)

= a³ + 2a²b + ab² + a²b + 2ab² + b³

= a³ + b³ + 3a²b + 3ab² proved!

here, a = x and b = 4

= (x + 4)³

= (x)³ + (4)³ + 3(x)²(4) + 3(x)(4)²

= x³ + 64 + 12x² + 48x

= x³ + 12x² + 48x + 64 final answer