Question
Factorise the following expressions.
$ a^3 x-x^4+a^2 x^2-a x^3 $
$ a^3 x-x^4+a^2 x^2-a x^3 $
✓
Answer
$ a^3 x-x^4+a^2 x^2-a x^3 $
$ =x\left(a^3-x^2+a^2 x-a x^2\right) $
$ =x\left(a^3+a^2 x-x^3-ax^2\right) $
$ =x\left[a^2(a+x)-x^2(x+?)\right] $
$ =x\left[(x+a)\left(a^2-x^2\right)\right] $
$ =x\left(a^2-x^2\right)(a+x) $
$ =x\left(a^3-x^2+a^2 x-a x^2\right) $
$ =x\left(a^3+a^2 x-x^3-ax^2\right) $
$ =x\left[a^2(a+x)-x^2(x+?)\right] $
$ =x\left[(x+a)\left(a^2-x^2\right)\right] $
$ =x\left(a^2-x^2\right)(a+x) $
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