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Popular >

expand ((x+y)^9)/((x-y)^5)

Solution

expand

\frac{( x + y ) ^{9}}{( x - y ) ^{5}}

Solution

\frac{x ^{9} + 9 x ^{8} y + 36 x ^{7} y ^{2} + 84 x ^{6} y ^{3} + 126 x ^{5} y ^{4} + 126 x ^{4} y ^{5} + 84 x ^{3} y ^{6} + 36 x ^{2} y ^{7} + 9 x y ^{8} + y ^{9}}{x ^{5} - 5 x ^{4} y + 10 x ^{3} y ^{2} - 10 x ^{2} y ^{3} + 5 x y ^{4} - y ^{5}}

Solution steps

\frac{( x + y ) ^{9}}{( x - y ) ^{5}}

(x - y)^{5} = x^{5} - 5 x^{4} y + 10 x^{3} y^{2} - 10 x^{2} y^{3} + 5 x y^{4} - y^{5}

= \frac{( x + y ) ^{9}}{x ^{5} - 5 x ^{4} y + 10 x ^{3} y ^{2} - 10 x ^{2} y ^{3} + 5 x y ^{4} - y ^{5}}

(x + y)^{9} = x^{9} + 9 x^{8} y + 36 x^{7} y^{2} + 84 x^{6} y^{3} + 126 x^{5} y^{4} + 126 x^{4} y^{5} + 84 x^{3} y^{6} + 36 x^{2} y^{7} + 9 x y^{8} + y^{9}

= \frac{x ^{9} + 9 x ^{8} y + 36 x ^{7} y ^{2} + 84 x ^{6} y ^{3} + 126 x ^{5} y ^{4} + 126 x ^{4} y ^{5} + 84 x ^{3} y ^{6} + 36 x ^{2} y ^{7} + 9 x y ^{8} + y ^{9}}{x ^{5} - 5 x ^{4} y + 10 x ^{3} y ^{2} - 10 x ^{2} y ^{3} + 5 x y ^{4} - y ^{5}}

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Frequently Asked Questions (FAQ)

What is expand ((x+y)^9)/((x-y)^5) ?
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