Question

$x^4-y^4$ divided by x-y we get

• A. $(x+y)(x^2+y^2)$
• B. x+y
• C. $x^2-y^2$
• D. $2y^4$

Answer 1

The correct option is A $(x+y)(x^2+y^2)$

Let $f\left(x\right)=x^4-y^4$ and factorise it as follows:

$f\left(x\right)=x^4-y^4=(x^2-y^2)(x^2+y^2)=(x-y)(x+y)(x^2+y^2)$

Therefore, $f\left(x\right)=(x-y)(x+y)(x^2+y^2)$

Let $g\left(x\right)=x-y$

Now divide $f\left(x\right)$ by $g\left(x\right)$ to get $q\left(x\right)$:

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

Hence, the quotient $q\left(x\right)=(x+y)(x^2+y^2)$.