What is expand (x^2(12+x^2)^2)/4 ?

The solution to expand (x^2(12+x^2)^2)/4 is (x^6)/4+6x^4+36x^2

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expand (x^2(12+x^2)^2)/4

expand

\frac{x ^{2} ( 12 + x ^{2} ) ^{2}}{4}

\frac{x ^{6}}{4} + 6 x^{4} + 36 x^{2}

Solution steps

\frac{x ^{2} ( 12 + x ^{2} ) ^{2}}{4}

(12 + x^{2})^{2} = 144 + 24 x^{2} + x^{4}

= \frac{x ^{2} ( x ^{4} + 24 x ^{2} + 144 )}{4}

Expand

x^{2} (144 + 24 x^{2} + x^{4}) : 144 x^{2} + 24 x^{4} + x^{6}

= \frac{144 x ^{2} + 24 x ^{4} + x ^{6}}{4}

Apply the fraction rule:

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

\frac{144 x ^{2} + 24 x ^{4} + x ^{6}}{4} = \frac{144 x ^{2}}{4} + \frac{24 x ^{4}}{4} + \frac{x ^{6}}{4}

= \frac{144 x ^{2}}{4} + \frac{24 x ^{4}}{4} + \frac{x ^{6}}{4}

Divide the numbers:

\frac{144}{4} = 36

= 36 x^{2} + \frac{24 x ^{4}}{4} + \frac{x ^{6}}{4}

Divide the numbers:

\frac{24}{4} = 6

= 36 x^{2} + 6 x^{4} + \frac{x ^{6}}{4}

Rewrite in standard form

= \frac{x ^{6}}{4} + 6 x^{4} + 36 x^{2}

1 + \frac{1325}{s ( s + 1.71 ) ( s + 100 )}

l c f (- 15, 10, - 5)

(e^{x^{2}} - 1)^{4}

\frac{32 ( 2 n + 1 ) ( n + 1 )}{3 n ^{2}}

(sin (x) + x cos (x)) (x + cos (x))

What is expand (x^2(12+x^2)^2)/4 ?
The solution to expand (x^2(12+x^2)^2)/4 is (x^6)/4+6x^4+36x^2