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Popular >

expand (2x-1/y)^9

Solution

expand

(2 x - \frac{1}{y})^{9}

Solution

512 x^{9} - \frac{2304 x ^{8}}{y} + \frac{4608 x ^{7}}{y ^{2}} - \frac{5376 x ^{6}}{y ^{3}} + \frac{4032 x ^{5}}{y ^{4}} - \frac{2016 x ^{4}}{y ^{5}} + \frac{672 x ^{3}}{y ^{6}} - \frac{144 x ^{2}}{y ^{7}} + \frac{18 x}{y ^{8}} - \frac{1}{y ^{9}}

Solution steps

(2 x - \frac{1}{y})^{9}

Apply binomial theorem:

(a + b)^{n} = i = 0 \sum n (i n) a^{(n - i)} b^{i}

a = 2 x, b = - \frac{1}{y}

= i = 0 \sum 9 (i 9) (2 x)^{(9 - i)} (- \frac{1}{y})^{i}

Expand summation

= \frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} (- \frac{1}{y})^{0} + \frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} (- \frac{1}{y})^{1} + \frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} (- \frac{1}{y})^{2} + \frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} (- \frac{1}{y})^{3} + \frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} (- \frac{1}{y})^{4} + \frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} (- \frac{1}{y})^{5} + \frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} (- \frac{1}{y})^{6} + \frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} (- \frac{1}{y})^{7} + \frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} (- \frac{1}{y})^{8} + \frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} (- \frac{1}{y})^{9}

Simplify

\frac{9 !}{0 ! ( 9 - 0 ) !} (2 x)^{9} (- \frac{1}{y})^{0} : 512 x^{9}

Simplify

\frac{9 !}{1 ! ( 9 - 1 ) !} (2 x)^{8} (- \frac{1}{y})^{1} : - \frac{2304 x ^{8}}{y}

Simplify

\frac{9 !}{2 ! ( 9 - 2 ) !} (2 x)^{7} (- \frac{1}{y})^{2} : \frac{4608 x ^{7}}{y ^{2}}

Simplify

\frac{9 !}{3 ! ( 9 - 3 ) !} (2 x)^{6} (- \frac{1}{y})^{3} : - \frac{5376 x ^{6}}{y ^{3}}

Simplify

\frac{9 !}{4 ! ( 9 - 4 ) !} (2 x)^{5} (- \frac{1}{y})^{4} : \frac{4032 x ^{5}}{y ^{4}}

Simplify

\frac{9 !}{5 ! ( 9 - 5 ) !} (2 x)^{4} (- \frac{1}{y})^{5} : - \frac{2016 x ^{4}}{y ^{5}}

Simplify

\frac{9 !}{6 ! ( 9 - 6 ) !} (2 x)^{3} (- \frac{1}{y})^{6} : \frac{672 x ^{3}}{y ^{6}}

Simplify

\frac{9 !}{7 ! ( 9 - 7 ) !} (2 x)^{2} (- \frac{1}{y})^{7} : - \frac{144 x ^{2}}{y ^{7}}

Simplify

\frac{9 !}{8 ! ( 9 - 8 ) !} (2 x)^{1} (- \frac{1}{y})^{8} : \frac{18 x}{y ^{8}}

Simplify

\frac{9 !}{9 ! ( 9 - 9 ) !} (2 x)^{0} (- \frac{1}{y})^{9} : - \frac{1}{y ^{9}}

= 512 x^{9} - \frac{2304 x ^{8}}{y} + \frac{4608 x ^{7}}{y ^{2}} - \frac{5376 x ^{6}}{y ^{3}} + \frac{4032 x ^{5}}{y ^{4}} - \frac{2016 x ^{4}}{y ^{5}} + \frac{672 x ^{3}}{y ^{6}} - \frac{144 x ^{2}}{y ^{7}} + \frac{18 x}{y ^{8}} - \frac{1}{y ^{9}}

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Frequently Asked Questions (FAQ)

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