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

The solution to expand (x(1-x^2)^2)/2 is (x^5)/2-x^3+x/2

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

expand

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

\frac{x ^{5}}{2} - x^{3} + \frac{x}{2}

Solution steps

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

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

= \frac{x ( x ^{4} - 2 x ^{2} + 1 )}{2}

Expand

x (1 - 2 x^{2} + x^{4}) : x - 2 x^{3} + x^{5}

= \frac{x - 2 x ^{3} + x ^{5}}{2}

Apply the fraction rule:

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

\frac{x - 2 x ^{3} + x ^{5}}{2} = \frac{x}{2} - \frac{2 x ^{3}}{2} + \frac{x ^{5}}{2}

= \frac{x}{2} - \frac{2 x ^{3}}{2} + \frac{x ^{5}}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{x}{2} - x^{3} + \frac{x ^{5}}{2}

Rewrite in standard form

= \frac{x ^{5}}{2} - x^{3} + \frac{x}{2}

(x + 2)^{2} + 3 (x + 1)^{'}

\frac{1}{( z + 3 ) ^{6}}

- \frac{30}{( 3 x + 1 ) ^{3}}

(2 x - 5 y = 7,) (4 x + 2 y = 2)

3 (3 x - 8 = 30)

What is expand (x(1-x^2)^2)/2 ?
The solution to expand (x(1-x^2)^2)/2 is (x^5)/2-x^3+x/2