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Popular >

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

Solution

expand

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

Solution

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

Solution steps

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

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

= \frac{x ^{4} + 2 x ^{2} + 1}{2}

Apply the fraction rule:

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

\frac{x ^{4} + 2 x ^{2} + 1}{2} = \frac{x ^{4}}{2} + \frac{2 x ^{2}}{2} + \frac{1}{2}

= \frac{x ^{4}}{2} + \frac{2 x ^{2}}{2} + \frac{1}{2}

Divide the numbers:

\frac{2}{2} = 1

= \frac{x ^{4}}{2} + x^{2} + \frac{1}{2}

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Frequently Asked Questions (FAQ)

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