Question
Factorise $: x^3 - 512$
✓
Answer
$x^3 - 512$
$= (x)^3 - (8)^3$
$= (x - 8)[(x)^2 + x \times 8 + (8)^2]$ Since $a^3 - b^3 = (a - b)(a^2 + a \times b + b^2)$
$= (x - 8)(x^2 + 8x + 64)$
$= x^3 + 8x^2 + 64x - 8x^2 - 64x - 512$
$= x^3 - 512$
$= (x)^3 - (8)^3$
$= (x - 8)[(x)^2 + x \times 8 + (8)^2]$ Since $a^3 - b^3 = (a - b)(a^2 + a \times b + b^2)$
$= (x - 8)(x^2 + 8x + 64)$
$= x^3 + 8x^2 + 64x - 8x^2 - 64x - 512$
$= x^3 - 512$
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