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Popular >

expand (2+8/5 x)^8

Solution

expand

(2 + \frac{8}{5} x)^{8}

Solution

256 + \frac{8192 x}{5} + \frac{114688 x ^{2}}{25} + \frac{917504 x ^{3}}{125} + \frac{917504 x ^{4}}{125} + \frac{14680064 x ^{5}}{3125} + \frac{29360128 x ^{6}}{15625} + \frac{33554432 x ^{7}}{78125} + \frac{16777216 x ^{8}}{390625}

Solution steps

(2 + \frac{8}{5} x)^{8}

Apply binomial theorem:

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

a = 2, b = \frac{8}{5} x

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

Expand summation

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

Simplify

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

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 2^{7} (\frac{8}{5} x)^{1} : \frac{8192 x}{5}

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 2^{6} (\frac{8}{5} x)^{2} : \frac{114688 x ^{2}}{25}

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 2^{5} (\frac{8}{5} x)^{3} : \frac{917504 x ^{3}}{125}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 2^{4} (\frac{8}{5} x)^{4} : \frac{917504 x ^{4}}{125}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 2^{3} (\frac{8}{5} x)^{5} : \frac{14680064 x ^{5}}{3125}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 2^{2} (\frac{8}{5} x)^{6} : \frac{29360128 x ^{6}}{15625}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 2^{1} (\frac{8}{5} x)^{7} : \frac{33554432 x ^{7}}{78125}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 2^{0} (\frac{8}{5} x)^{8} : \frac{16777216 x ^{8}}{390625}

= 256 + \frac{8192 x}{5} + \frac{114688 x ^{2}}{25} + \frac{917504 x ^{3}}{125} + \frac{917504 x ^{4}}{125} + \frac{14680064 x ^{5}}{3125} + \frac{29360128 x ^{6}}{15625} + \frac{33554432 x ^{7}}{78125} + \frac{16777216 x ^{8}}{390625}

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Frequently Asked Questions (FAQ)

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