Question
Factorise:
$(x + 2)^3 - (x - 2)^3$
$(x + 2)^3 - (x - 2)^3$
✓
Answer
$(x + 2)^3 - (x - 2)^3$
$= [(x + 2) - (x - 2)][(x + 2)^2 + (x + 2)(x - 2) + (x - 2)^2]$
$= 4(x^2 + 4x + 4 + x^2 - 4 + x^2 - 4x + 4)$
$= 4(3x^2 + 4)$
$= [(x + 2) - (x - 2)][(x + 2)^2 + (x + 2)(x - 2) + (x - 2)^2]$
$= 4(x^2 + 4x + 4 + x^2 - 4 + x^2 - 4x + 4)$
$= 4(3x^2 + 4)$
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