What is expand ((x^2-5)^3)/(125) ?

The solution to expand ((x^2-5)^3)/(125) is (x^6}{125}-(3x^4)/(25)+\frac{3x^2)/5-1

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expand ((x^2-5)^3)/(125)

expand

\frac{( x ^{2} - 5 ) ^{3}}{125}

\frac{x ^{6}}{125} - \frac{3 x ^{4}}{25} + \frac{3 x ^{2}}{5} - 1

Solution steps

\frac{( x ^{2} - 5 ) ^{3}}{125}

(x^{2} - 5)^{3} = x^{6} - 15 x^{4} + 75 x^{2} - 125

= \frac{x ^{6} - 15 x ^{4} + 75 x ^{2} - 125}{125}

Apply the fraction rule:

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

\frac{x ^{6} - 15 x ^{4} + 75 x ^{2} - 125}{125} = \frac{x ^{6}}{125} - \frac{15 x ^{4}}{125} + \frac{75 x ^{2}}{125} - \frac{125}{125}

= \frac{x ^{6}}{125} - \frac{15 x ^{4}}{125} + \frac{75 x ^{2}}{125} - \frac{125}{125}

Apply rule

\frac{a}{a} = 1

\frac{125}{125} = 1

= \frac{x ^{6}}{125} - \frac{15 x ^{4}}{125} + \frac{75 x ^{2}}{125} - 1

Cancel

\frac{15 x ^{4}}{125} : \frac{3 x ^{4}}{25}

= \frac{x ^{6}}{125} - \frac{3 x ^{4}}{25} + \frac{75 x ^{2}}{125} - 1

Cancel

\frac{75 x ^{2}}{125} : \frac{3 x ^{2}}{5}

= \frac{x ^{6}}{125} - \frac{3 x ^{4}}{25} + \frac{3 x ^{2}}{5} - 1

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What is expand ((x^2-5)^3)/(125) ?
The solution to expand ((x^2-5)^3)/(125) is (x^6}{125}-(3x^4)/(25)+\frac{3x^2)/5-1