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Popular >

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

Solution

expand

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

Solution

\frac{x ^{8}}{256} - \frac{x ^{7}}{32} + \frac{7 x ^{6}}{64} - \frac{7 x ^{5}}{32} + \frac{35 x ^{4}}{128} - \frac{7 x ^{3}}{32} + \frac{7 x ^{2}}{64} - \frac{x}{32} + \frac{1}{256}

Solution steps

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

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

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

(1 - x)^{8} = 1 - 8 x + 28 x^{2} - 56 x^{3} + 70 x^{4} - 56 x^{5} + 28 x^{6} - 8 x^{7} + x^{8}

= \frac{1 - 8 x + 28 x ^{2} - 56 x ^{3} + 70 x ^{4} - 56 x ^{5} + 28 x ^{6} - 8 x ^{7} + x ^{8}}{2 ^{8}}

2^{8} = 256

= \frac{1 - 8 x + 28 x ^{2} - 56 x ^{3} + 70 x ^{4} - 56 x ^{5} + 28 x ^{6} - 8 x ^{7} + x ^{8}}{256}

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{1 - 8 x + 28 x ^{2} - 56 x ^{3} + 70 x ^{4} - 56 x ^{5} + 28 x ^{6} - 8 x ^{7} + x ^{8}}{256} = \frac{1}{256} - \frac{8 x}{256} + \frac{28 x ^{2}}{256} - \frac{56 x ^{3}}{256} + \frac{70 x ^{4}}{256} - \frac{56 x ^{5}}{256} + \frac{28 x ^{6}}{256} - \frac{8 x ^{7}}{256} + \frac{x ^{8}}{256}

= \frac{1}{256} - \frac{8 x}{256} + \frac{28 x ^{2}}{256} - \frac{56 x ^{3}}{256} + \frac{70 x ^{4}}{256} - \frac{56 x ^{5}}{256} + \frac{28 x ^{6}}{256} - \frac{8 x ^{7}}{256} + \frac{x ^{8}}{256}

\frac{8 x}{256} = \frac{x}{32}

\frac{28 x ^{2}}{256} = \frac{7 x ^{2}}{64}

\frac{56 x ^{3}}{256} = \frac{7 x ^{3}}{32}

\frac{70 x ^{4}}{256} = \frac{35 x ^{4}}{128}

\frac{56 x ^{5}}{256} = \frac{7 x ^{5}}{32}

\frac{28 x ^{6}}{256} = \frac{7 x ^{6}}{64}

\frac{8 x ^{7}}{256} = \frac{x ^{7}}{32}

= \frac{1}{256} - \frac{x}{32} + \frac{7 x ^{2}}{64} - \frac{7 x ^{3}}{32} + \frac{35 x ^{4}}{128} - \frac{7 x ^{5}}{32} + \frac{7 x ^{6}}{64} - \frac{x ^{7}}{32} + \frac{x ^{8}}{256}

Rewrite in standard form

= \frac{x ^{8}}{256} - \frac{x ^{7}}{32} + \frac{7 x ^{6}}{64} - \frac{7 x ^{5}}{32} + \frac{35 x ^{4}}{128} - \frac{7 x ^{3}}{32} + \frac{7 x ^{2}}{64} - \frac{x}{32} + \frac{1}{256}

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Frequently Asked Questions (FAQ)

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