Question

How do you factor `x^3 - y^6`?

Answer 1

`(sqrtx-y)(sqrtx+y)(x^2+xy^2+y^4)`

Explanation:

`"this can be expressed as a "color(blue)"difference of cubes"`

`•color(white)(x)a^3-b^3=(a-b)(a^2+ab+b^2)`

`"with "a=x" and "b=y^2to(y^2)^3=y^6`

`=(x-y^2)(x^2+xy^2+y^4)`

`"we can express "x-y^2" as a "color(blue)"difference of squares"`

`•color(white)(x)a^2-b^2=(a-b)(a+b)`

`"with "a=sqrtx" and "b=y`

`=(sqrtx-y)(sqrtx+y)`

`rArrx^3-y^6=(sqrtx-y)(sqrtx+y)(x^2+xy^2+y^4)`