What is expand ((1-x^2)^3)/3 ?

The solution to expand ((1-x^2)^3)/3 is -(x^6)/3+x^4-x^2+1/3

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expand ((1-x^2)^3)/3

expand

\frac{( 1 - x ^{2} ) ^{3}}{3}

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

Solution steps

\frac{( 1 - x ^{2} ) ^{3}}{3}

(1 - x^{2})^{3} = 1 - 3 x^{2} + 3 x^{4} - x^{6}

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{3}{3} = 1

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

Rewrite in standard form

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

(4 x + 4)^{2}

(- cot (x) csc (x)) (2 csc (x) - 1)

(y + Δ)^{3}

\frac{x ^{4} + y ^{4}}{x y ( y ^{2} + x ^{2} )}

What is expand ((1-x^2)^3)/3 ?
The solution to expand ((1-x^2)^3)/3 is -(x^6)/3+x^4-x^2+1/3