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Popular >

expand (2+5/8 x)^8

Solution

expand

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

Solution

256 + 640 x + 700 x^{2} + \frac{875 x ^{3}}{2} + \frac{21875 x ^{4}}{128} + \frac{21875 x ^{5}}{512} + \frac{109375 x ^{6}}{16384} + \frac{78125 x ^{7}}{131072} + \frac{390625 x ^{8}}{16777216}

Solution steps

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

Apply binomial theorem:

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

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

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

Expand summation

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

Simplify

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

Simplify

\frac{8 !}{1 ! ( 8 - 1 ) !} \cdot 2^{7} (\frac{5}{8} x)^{1} : 640 x

Simplify

\frac{8 !}{2 ! ( 8 - 2 ) !} \cdot 2^{6} (\frac{5}{8} x)^{2} : 700 x^{2}

Simplify

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

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 2^{4} (\frac{5}{8} x)^{4} : \frac{21875 x ^{4}}{128}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 2^{3} (\frac{5}{8} x)^{5} : \frac{21875 x ^{5}}{512}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 2^{2} (\frac{5}{8} x)^{6} : \frac{109375 x ^{6}}{16384}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 2^{1} (\frac{5}{8} x)^{7} : \frac{78125 x ^{7}}{131072}

Simplify

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

= 256 + 640 x + 700 x^{2} + \frac{875 x ^{3}}{2} + \frac{21875 x ^{4}}{128} + \frac{21875 x ^{5}}{512} + \frac{109375 x ^{6}}{16384} + \frac{78125 x ^{7}}{131072} + \frac{390625 x ^{8}}{16777216}

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Frequently Asked Questions (FAQ)

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