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Popular >

expand (3x+(7/8)/x)^8

Solution

expand

(3 x + \frac{\frac{7}{8}}{x})^{8}

Solution

6561 x^{8} + 15309 x^{6} + \frac{250047 x ^{4}}{16} + \frac{583443 x ^{2}}{64} + \frac{6806835}{2048} + \frac{3176523}{4096 x ^{2}} + \frac{7411887}{65536 x ^{4}} + \frac{2470629}{262144 x ^{6}} + \frac{5764801}{16777216 x ^{8}}

Solution steps

(3 x + \frac{\frac{7}{8}}{x})^{8}

Apply binomial theorem:

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

a = 3 x, b = \frac{\frac{7}{8}}{x}

= i = 0 \sum 8 (i 8) (3 x)^{(8 - i)} (\frac{\frac{7}{8}}{x})^{i}

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} (3 x)^{8} (\frac{\frac{7}{8}}{x})^{0} : 6561 x^{8}

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} (3 x)^{7} (\frac{\frac{7}{8}}{x})^{1} : 15309 x^{6}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} (3 x)^{6} (\frac{\frac{7}{8}}{x})^{2} : \frac{250047 x ^{4}}{16}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} (3 x)^{5} (\frac{\frac{7}{8}}{x})^{3} : \frac{583443 x ^{2}}{64}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} (3 x)^{4} (\frac{\frac{7}{8}}{x})^{4} : \frac{6806835}{2048}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} (3 x)^{3} (\frac{\frac{7}{8}}{x})^{5} : \frac{3176523}{4096 x ^{2}}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} (3 x)^{2} (\frac{\frac{7}{8}}{x})^{6} : \frac{7411887}{65536 x ^{4}}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} (3 x)^{1} (\frac{\frac{7}{8}}{x})^{7} : \frac{2470629}{262144 x ^{6}}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} (3 x)^{0} (\frac{\frac{7}{8}}{x})^{8} : \frac{5764801}{16777216 x ^{8}}

= 6561 x^{8} + 15309 x^{6} + \frac{250047 x ^{4}}{16} + \frac{583443 x ^{2}}{64} + \frac{6806835}{2048} + \frac{3176523}{4096 x ^{2}} + \frac{7411887}{65536 x ^{4}} + \frac{2470629}{262144 x ^{6}} + \frac{5764801}{16777216 x ^{8}}

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