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

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

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

expand

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

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

Solution steps

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

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

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{2}{2} = 1

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

Rewrite in standard form

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

- 4 (3 - 4 x) - 2 (x - 1 = 12 x)

A (3, - 1) B (5, 2)

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

12 (\frac{X - 7}{4} + \frac{25 ( X - 2 )}{3} = \frac{5 X + 35}{4} + \frac{5}{2} (X - 7))

f (x) (\frac{2 ( x - 1 )}{3} + \frac{3 ( 2 x + 1 )}{9} = 9)

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