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Popular >

expand (1+5/8 x)^8

Solution

expand

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

Solution

1 + 5 x + \frac{175 x ^{2}}{16} + \frac{875 x ^{3}}{64} + \frac{21875 x ^{4}}{2048} + \frac{21875 x ^{5}}{4096} + \frac{109375 x ^{6}}{65536} + \frac{78125 x ^{7}}{262144} + \frac{390625 x ^{8}}{16777216}

Solution steps

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

Apply binomial theorem:

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

a = 1, b = \frac{5}{8} x

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

Expand summation

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

Simplify

\frac{8 !}{0 ! ( 8 - 0 ) !} \cdot 1^{8} (\frac{5}{8} x)^{0} : 1

Simplify

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

Simplify

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

Simplify

\frac{8 !}{3 ! ( 8 - 3 ) !} \cdot 1^{5} (\frac{5}{8} x)^{3} : \frac{875 x ^{3}}{64}

Simplify

\frac{8 !}{4 ! ( 8 - 4 ) !} \cdot 1^{4} (\frac{5}{8} x)^{4} : \frac{21875 x ^{4}}{2048}

Simplify

\frac{8 !}{5 ! ( 8 - 5 ) !} \cdot 1^{3} (\frac{5}{8} x)^{5} : \frac{21875 x ^{5}}{4096}

Simplify

\frac{8 !}{6 ! ( 8 - 6 ) !} \cdot 1^{2} (\frac{5}{8} x)^{6} : \frac{109375 x ^{6}}{65536}

Simplify

\frac{8 !}{7 ! ( 8 - 7 ) !} \cdot 1^{1} (\frac{5}{8} x)^{7} : \frac{78125 x ^{7}}{262144}

Simplify

\frac{8 !}{8 ! ( 8 - 8 ) !} \cdot 1^{0} (\frac{5}{8} x)^{8} : \frac{390625 x ^{8}}{16777216}

= 1 + 5 x + \frac{175 x ^{2}}{16} + \frac{875 x ^{3}}{64} + \frac{21875 x ^{4}}{2048} + \frac{21875 x ^{5}}{4096} + \frac{109375 x ^{6}}{65536} + \frac{78125 x ^{7}}{262144} + \frac{390625 x ^{8}}{16777216}

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Frequently Asked Questions (FAQ)

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