What is ((x^5+y^5))/((x+y)) ?

The solution to ((x^5+y^5))/((x+y)) is x^4-x^3y+x^2y^2-xy^3+y^4

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simplify ((x^5+y^5))/((x+y))

simplify

\frac{( x ^{5} + y ^{5} )}{( x + y )}

x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}

Solution steps

\frac{x ^{5} + y ^{5}}{x + y}

Apply factoring rule:

x^{n} + y^{n} = (x + y) (x^{n - 1} - x^{n - 2} y + \dots - x y^{n - 2} + y^{n - 1}), n i s o dd

x^{5} + y^{5} = (x + y) (x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4})

= \frac{( x + y ) ( x ^{4} - x ^{3} y + x ^{2} y ^{2} - x y ^{3} + y ^{4} )}{x + y}

Cancel the common factor:

x + y

= x^{4} - x^{3} y + x^{2} y^{2} - x y^{3} + y^{4}

\frac{x + 4}{2} + \frac{x + 1}{3}

\frac{\frac{2 a + 1}{10 a - 5}}{\frac{10 a}{4 a ^{2} - 1}}

- x (5 x - 4)

15 \cdot 20

What is ((x^5+y^5))/((x+y)) ?
The solution to ((x^5+y^5))/((x+y)) is x^4-x^3y+x^2y^2-xy^3+y^4