What is expand ((6-x)^4)/(81) ?

The solution to expand ((6-x)^4)/(81) is (x^4}{81}-(8x^3)/(27)+\frac{8x^2)/3-(32x)/3+16

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expand ((6-x)^4)/(81)

expand

\frac{( 6 - x ) ^{4}}{81}

\frac{x ^{4}}{81} - \frac{8 x ^{3}}{27} + \frac{8 x ^{2}}{3} - \frac{32 x}{3} + 16

Solution steps

\frac{( 6 - x ) ^{4}}{81}

(6 - x)^{4} = 1296 - 864 x + 216 x^{2} - 24 x^{3} + x^{4}

= \frac{1296 - 864 x + 216 x ^{2} - 24 x ^{3} + x ^{4}}{81}

Apply the fraction rule:

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

\frac{1296 - 864 x + 216 x ^{2} - 24 x ^{3} + x ^{4}}{81} = \frac{1296}{81} - \frac{864 x}{81} + \frac{216 x ^{2}}{81} - \frac{24 x ^{3}}{81} + \frac{x ^{4}}{81}

= \frac{1296}{81} - \frac{864 x}{81} + \frac{216 x ^{2}}{81} - \frac{24 x ^{3}}{81} + \frac{x ^{4}}{81}

\frac{1296}{81} = 16

\frac{864 x}{81} = \frac{32 x}{3}

\frac{216 x ^{2}}{81} = \frac{8 x ^{2}}{3}

\frac{24 x ^{3}}{81} = \frac{8 x ^{3}}{27}

= 16 - \frac{32 x}{3} + \frac{8 x ^{2}}{3} - \frac{8 x ^{3}}{27} + \frac{x ^{4}}{81}

Rewrite in standard form

= \frac{x ^{4}}{81} - \frac{8 x ^{3}}{27} + \frac{8 x ^{2}}{3} - \frac{32 x}{3} + 16

(x^{3} + \frac{1}{x ^{3}}) (x^{3} - \frac{1}{x ^{3}})

\frac{x + 4}{( x + 5 ) ( x - 1 )}

\frac{2 s ^{2} - 6 s + 5}{( s - 1 ) ( s - 2 ) ( s - 3 )}

\frac{x + 3}{x ( x + 7 )}

What is expand ((6-x)^4)/(81) ?
The solution to expand ((6-x)^4)/(81) is (x^4}{81}-(8x^3)/(27)+\frac{8x^2)/3-(32x)/3+16