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Popular >

expand (5x-1/(2x^3))^8

Solution

expand

(5 x - \frac{1}{2 x ^{3}})^{8}

Solution

390625 x^{8} - 312500 x^{4} + 109375 - \frac{21875}{x ^{4}} + \frac{21875}{8 x ^{8}} - \frac{875}{4 x ^{12}} + \frac{175}{16 x ^{16}} - \frac{5}{16 x ^{20}} + \frac{1}{256 x ^{24}}

Solution steps

(5 x - \frac{1}{2 x ^{3}})^{8}

Apply binomial theorem:

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

a = 5 x, b = - \frac{1}{2 x ^{3}}

= i = 0 \sum 8 (i 8) (5 x)^{(8 - i)} (- \frac{1}{2 x ^{3}})^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (5 x)^{8} (- \frac{1}{2 x ^{3}})^{0} : 390625 x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (5 x)^{7} (- \frac{1}{2 x ^{3}})^{1} : - 312500 x^{4}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (5 x)^{6} (- \frac{1}{2 x ^{3}})^{2} : 109375

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (5 x)^{5} (- \frac{1}{2 x ^{3}})^{3} : - \frac{21875}{x ^{4}}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (5 x)^{4} (- \frac{1}{2 x ^{3}})^{4} : \frac{21875}{8 x ^{8}}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (5 x)^{3} (- \frac{1}{2 x ^{3}})^{5} : - \frac{875}{4 x ^{12}}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (5 x)^{2} (- \frac{1}{2 x ^{3}})^{6} : \frac{175}{16 x ^{16}}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (5 x)^{1} (- \frac{1}{2 x ^{3}})^{7} : - \frac{5}{16 x ^{20}}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (5 x)^{0} (- \frac{1}{2 x ^{3}})^{8} : \frac{1}{256 x ^{24}}

= 390625 x^{8} - 312500 x^{4} + 109375 - \frac{21875}{x ^{4}} + \frac{21875}{8 x ^{8}} - \frac{875}{4 x ^{12}} + \frac{175}{16 x ^{16}} - \frac{5}{16 x ^{20}} + \frac{1}{256 x ^{24}}

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Frequently Asked Questions (FAQ)

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