Question
Factorise:
$x-8 x y^3$
$x-8 x y^3$
✓
Answer
$x-8 x y^3$
$=x\left(1-8 y^3\right)$
$=x\left[(1)^3-(2 y)^3\right]$
$=x(1-2 y)\left[(1)^2+1 \times 2 y+(2 y)^2\right] \text { Since } a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
$=x(1-2 y)\left(1+2 y+4 y^2\right)$
$=x\left(1-8 y^3\right)$
$=x\left[(1)^3-(2 y)^3\right]$
$=x(1-2 y)\left[(1)^2+1 \times 2 y+(2 y)^2\right] \text { Since } a^3-b^3=(a-b)\left(a^2+a \times b+b^2\right)$
$=x(1-2 y)\left(1+2 y+4 y^2\right)$
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