Question

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

Answer 1

`(x^5+y^5)/(x+y)=x^4-x^3y+x^2y^2-xy^3+y^4`

Explanation:

Given the expression

`\left(x^5+y^5\right)/ \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)`

`=(\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,

`(x^5+y^5)/(x+y)=x^4-x^3y+x^2y^2-xy^3+y^4`