Factorise: $x^{3} + x^{2} - 4 x - 4$

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Solution

$x^{3} + x^{2} - 4 x - 4$
$= x^{2} (x + 1) - 4 (x + 1)$
$= (x + 1) (x^{2} - 4)$
$= (x + 1) (x^{2} - 2^{2})$
$= (x + 1) (x + 2) (x - 2),$ $∵ a^{2} - b^{2} = (a - b) (a + b)$

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Factorise: x3+x2−4x−4

x3+x2−4x−4=x2(x+1)−4(x+1)=(x+1)(x2−4)=(x+1)(x2−22)=(x+1)(x+2)(x−2), ∵a2−b2=(a−b)(a+b)

Factorise: $x^{3} + x^{2} - 4 x - 4$

$x^{3} + x^{2} - 4 x - 4$
$= x^{2} (x + 1) - 4 (x + 1)$
$= (x + 1) (x^{2} - 4)$
$= (x + 1) (x^{2} - 2^{2})$
$= (x + 1) (x + 2) (x - 2),$ $∵ a^{2} - b^{2} = (a - b) (a + b)$