Question

Divide: $(x^4-y^4)$ by $(x-y)$. Is $(x-y)$ a factor of $(x^4-y^4)$?

Answer 1

As we know that $x^2-y^2=(x+y)(x-y)$

Then using this formula we simplify this expression as:

$x^4-y^4=(x^2{)}^2-(y^2{)}^2=(x^2+y^2)(x^2-y^2)=(x^2+y^2)(x+y)(x-y)$

Then dividing the expression by x-y we have:

$\frac{(x^2+y^2)(x+y)(x-y)}{x-y}=(x^2+y^2)(x+y)$

Hence, it a factor of $x^4-y^4$