What is (x^7+y^7)/(x+y) ?

The solution to (x^7+y^7)/(x+y) is x^6-x^5y+x^4y^2-x^3y^3+x^2y^4-xy^5+y^6

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simplify (x^7+y^7)/(x+y)

simplify

\frac{x ^{7} + y ^{7}}{x + y}

x^{6} - x^{5} y + x^{4} y^{2} - x^{3} y^{3} + x^{2} y^{4} - x y^{5} + y^{6}

Solution steps

\frac{x ^{7} + y ^{7}}{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^{7} + y^{7} = (x + y) (x^{6} - x^{5} y + x^{4} y^{2} - x^{3} y^{3} + x^{2} y^{4} - x y^{5} + y^{6})

= \frac{( x + y ) ( x ^{6} - x ^{5} y + x ^{4} y ^{2} - x ^{3} y ^{3} + x ^{2} y ^{4} - x y ^{5} + y ^{6} )}{x + y}

Cancel the common factor:

x + y

= x^{6} - x^{5} y + x^{4} y^{2} - x^{3} y^{3} + x^{2} y^{4} - x y^{5} + y^{6}

\frac{9}{2} + 4

\frac{9}{2} - 5

- 12 \cdot (- 8)

(2) (- 4)

What is (x^7+y^7)/(x+y) ?
The solution to (x^7+y^7)/(x+y) is x^6-x^5y+x^4y^2-x^3y^3+x^2y^4-xy^5+y^6