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

The solution to expand (5(2-x^2)^2)/2 is (5x^4)/2-10x^2+10

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

expand

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

\frac{5 x ^{4}}{2} - 10 x^{2} + 10

Solution steps

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

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

= \frac{5 ( x ^{4} - 4 x ^{2} + 4 )}{2}

Expand

5 (4 - 4 x^{2} + x^{4}) : 20 - 20 x^{2} + 5 x^{4}

= \frac{20 - 20 x ^{2} + 5 x ^{4}}{2}

Apply the fraction rule:

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

\frac{20 - 20 x ^{2} + 5 x ^{4}}{2} = \frac{20}{2} - \frac{20 x ^{2}}{2} + \frac{5 x ^{4}}{2}

= \frac{20}{2} - \frac{20 x ^{2}}{2} + \frac{5 x ^{4}}{2}

Divide the numbers:

\frac{20}{2} = 10

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

Rewrite in standard form

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

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

(x - 9) x + 6

(e^{2 x} + 4)^{2}

2 (cos (t)) (1 - t) (7 - t^{3})

What is expand (5(2-x^2)^2)/2 ?
The solution to expand (5(2-x^2)^2)/2 is (5x^4)/2-10x^2+10