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