What is expand ((x^2-1)^5)/(10) ?

The solution to expand ((x^2-1)^5)/(10) is (x^{10}}{10}-\frac{x^8)/2+x^6-x^4+(x^2)/2-1/10

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expand ((x^2-1)^5)/(10)

expand

\frac{( x ^{2} - 1 ) ^{5}}{10}

\frac{x ^{10}}{10} - \frac{x ^{8}}{2} + x^{6} - x^{4} + \frac{x ^{2}}{2} - \frac{1}{10}

Solution steps

\frac{( x ^{2} - 1 ) ^{5}}{10}

(x^{2} - 1)^{5} = x^{10} - 5 x^{8} + 10 x^{6} - 10 x^{4} + 5 x^{2} - 1

= \frac{x ^{10} - 5 x ^{8} + 10 x ^{6} - 10 x ^{4} + 5 x ^{2} - 1}{10}

Apply the fraction rule:

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

\frac{x ^{10} - 5 x ^{8} + 10 x ^{6} - 10 x ^{4} + 5 x ^{2} - 1}{10} = \frac{x ^{10}}{10} - \frac{5 x ^{8}}{10} + \frac{10 x ^{6}}{10} - \frac{10 x ^{4}}{10} + \frac{5 x ^{2}}{10} - \frac{1}{10}

= \frac{x ^{10}}{10} - \frac{5 x ^{8}}{10} + \frac{10 x ^{6}}{10} - \frac{10 x ^{4}}{10} + \frac{5 x ^{2}}{10} - \frac{1}{10}

\frac{5 x ^{8}}{10} = \frac{x ^{8}}{2}

\frac{10 x ^{6}}{10} = x^{6}

\frac{10 x ^{4}}{10} = x^{4}

\frac{5 x ^{2}}{10} = \frac{x ^{2}}{2}

= \frac{x ^{10}}{10} - \frac{x ^{8}}{2} + x^{6} - x^{4} + \frac{x ^{2}}{2} - \frac{1}{10}

x (x - a) (x - b) (x - c) + a + c

\frac{5 ( 2 a + b )}{3 b}

\frac{1}{( x - 2 ) ( a - b )}

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

14 x 2 - 38 x - 72

What is expand ((x^2-1)^5)/(10) ?
The solution to expand ((x^2-1)^5)/(10) is (x^{10}}{10}-\frac{x^8)/2+x^6-x^4+(x^2)/2-1/10