Question

(x5 + y5) ÷ (x + y) please answer ASAP

Answer 1

Answer:

$\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4$

Step-by-step explanation:

Given the expression

$\left(x^5+y^5\right)\div \left(x+y\right)$

$\mathrm{Apply\:factoring\:rule:\:}x^n+y^n=\left(x+y\right)\left(x^{n-1}-x^{n-2}y+\:\dots \:-\:xy^{n-2}\:+\:y^{n-1}\right)\:\quad \quad \mathrm{n\:is\:odd}$

$x^5+y^5=\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)$

$=\frac{\left(x+y\right)\left(x^4-x^3y+x^2y^2-xy^3+y^4\right)}{x+y}$

Cancel the common factor: x+y

$=x^4-x^3y+x^2y^2-xy^3+y^4$

Thus,

$\frac{x^5+y^5}{x+y}=x^4-x^3y+x^2y^2-xy^3+y^4$