What is expand (a^2(12a^2-5)^2)/4 ?

The solution to expand (a^2(12a^2-5)^2)/4 is 36a^6-30a^4+(25a^2)/4

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expand (a^2(12a^2-5)^2)/4

expand

\frac{a ^{2} ( 12 a ^{2} - 5 ) ^{2}}{4}

36 a^{6} - 30 a^{4} + \frac{25 a ^{2}}{4}

Solution steps

\frac{a ^{2} ( 12 a ^{2} - 5 ) ^{2}}{4}

(12 a^{2} - 5)^{2} = 144 a^{4} - 120 a^{2} + 25

= \frac{a ^{2} ( 144 a ^{4} - 120 a ^{2} + 25 )}{4}

Expand

a^{2} (144 a^{4} - 120 a^{2} + 25) : 144 a^{6} - 120 a^{4} + 25 a^{2}

= \frac{144 a ^{6} - 120 a ^{4} + 25 a ^{2}}{4}

Apply the fraction rule:

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

\frac{144 a ^{6} - 120 a ^{4} + 25 a ^{2}}{4} = \frac{144 a ^{6}}{4} - \frac{120 a ^{4}}{4} + \frac{25 a ^{2}}{4}

= \frac{144 a ^{6}}{4} - \frac{120 a ^{4}}{4} + \frac{25 a ^{2}}{4}

Divide the numbers:

\frac{144}{4} = 36

= 36 a^{6} - \frac{120 a ^{4}}{4} + \frac{25 a ^{2}}{4}

Divide the numbers:

\frac{120}{4} = 30

= 36 a^{6} - 30 a^{4} + \frac{25 a ^{2}}{4}

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What is expand (a^2(12a^2-5)^2)/4 ?
The solution to expand (a^2(12a^2-5)^2)/4 is 36a^6-30a^4+(25a^2)/4