What is expand ((2-x)^4)/(16) ?

The solution to expand ((2-x)^4)/(16) is (x^4}{16}-\frac{x^3)/2+(3x^2)/2-2x+1

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expand ((2-x)^4)/(16)

expand

\frac{( 2 - x ) ^{4}}{16}

\frac{x ^{4}}{16} - \frac{x ^{3}}{2} + \frac{3 x ^{2}}{2} - 2 x + 1

Solution steps

\frac{( 2 - x ) ^{4}}{16}

(2 - x)^{4} = 16 - 32 x + 24 x^{2} - 8 x^{3} + x^{4}

= \frac{16 - 32 x + 24 x ^{2} - 8 x ^{3} + x ^{4}}{16}

Apply the fraction rule:

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

\frac{16 - 32 x + 24 x ^{2} - 8 x ^{3} + x ^{4}}{16} = \frac{16}{16} - \frac{32 x}{16} + \frac{24 x ^{2}}{16} - \frac{8 x ^{3}}{16} + \frac{x ^{4}}{16}

= \frac{16}{16} - \frac{32 x}{16} + \frac{24 x ^{2}}{16} - \frac{8 x ^{3}}{16} + \frac{x ^{4}}{16}

Apply rule

\frac{a}{a} = 1

\frac{16}{16} = 1

= 1 - \frac{32 x}{16} + \frac{24 x ^{2}}{16} - \frac{8 x ^{3}}{16} + \frac{x ^{4}}{16}

Divide the numbers:

\frac{32}{16} = 2

= 1 - 2 x + \frac{24 x ^{2}}{16} - \frac{8 x ^{3}}{16} + \frac{x ^{4}}{16}

Cancel

\frac{24 x ^{2}}{16} : \frac{3 x ^{2}}{2}

= 1 - 2 x + \frac{3 x ^{2}}{2} - \frac{8 x ^{3}}{16} + \frac{x ^{4}}{16}

Cancel

\frac{8 x ^{3}}{16} : \frac{x ^{3}}{2}

= 1 - 2 x + \frac{3 x ^{2}}{2} - \frac{x ^{3}}{2} + \frac{x ^{4}}{16}

Rewrite in standard form

= \frac{x ^{4}}{16} - \frac{x ^{3}}{2} + \frac{3 x ^{2}}{2} - 2 x + 1

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What is expand ((2-x)^4)/(16) ?
The solution to expand ((2-x)^4)/(16) is (x^4}{16}-\frac{x^3)/2+(3x^2)/2-2x+1