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Popular >

expand (3/x-x/3)^8

Solution

expand

(\frac{3}{x} - \frac{x}{3})^{8}

Solution

\frac{6561}{x ^{8}} - \frac{5832}{x ^{6}} + \frac{2268}{x ^{4}} - \frac{504}{x ^{2}} + 70 - \frac{56 x ^{2}}{9} + \frac{28 x ^{4}}{81} - \frac{8 x ^{6}}{729} + \frac{x ^{8}}{6561}

Solution steps

(\frac{3}{x} - \frac{x}{3})^{8}

Apply binomial theorem:

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

a = \frac{3}{x}, b = - \frac{x}{3}

= i = 0 \sum 8 (i 8) (\frac{3}{x})^{(8 - i)} (- \frac{x}{3})^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (\frac{3}{x})^{8} (- \frac{x}{3})^{0} : \frac{6561}{x ^{8}}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (\frac{3}{x})^{7} (- \frac{x}{3})^{1} : - \frac{5832}{x ^{6}}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (\frac{3}{x})^{6} (- \frac{x}{3})^{2} : \frac{2268}{x ^{4}}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (\frac{3}{x})^{5} (- \frac{x}{3})^{3} : - \frac{504}{x ^{2}}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (\frac{3}{x})^{4} (- \frac{x}{3})^{4} : 70

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (\frac{3}{x})^{3} (- \frac{x}{3})^{5} : - \frac{56 x ^{2}}{9}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (\frac{3}{x})^{2} (- \frac{x}{3})^{6} : \frac{28 x ^{4}}{81}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (\frac{3}{x})^{1} (- \frac{x}{3})^{7} : - \frac{8 x ^{6}}{729}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (\frac{3}{x})^{0} (- \frac{x}{3})^{8} : \frac{x ^{8}}{6561}

= \frac{6561}{x ^{8}} - \frac{5832}{x ^{6}} + \frac{2268}{x ^{4}} - \frac{504}{x ^{2}} + 70 - \frac{56 x ^{2}}{9} + \frac{28 x ^{4}}{81} - \frac{8 x ^{6}}{729} + \frac{x ^{8}}{6561}

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Frequently Asked Questions (FAQ)

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