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{( x ^{2} + 5 x - 36 )}{( x + 9 )}

- 3 a^{4} + 15 a^{2} + 108

\frac{3 ^{- 1}}{3 ^{4}}

\frac{0}{- 15}

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