What is expand (x^6(x^2-8)^3)/3 ?

The solution to expand (x^6(x^2-8)^3)/3 is (x^{12})/3-8x^{10}+64x^8-(512x^6)/3

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expand (x^6(x^2-8)^3)/3

expand

\frac{x ^{6} ( x ^{2} - 8 ) ^{3}}{3}

\frac{x ^{12}}{3} - 8 x^{10} + 64 x^{8} - \frac{512 x ^{6}}{3}

Solution steps

\frac{x ^{6} ( x ^{2} - 8 ) ^{3}}{3}

(x^{2} - 8)^{3} = x^{6} - 24 x^{4} + 192 x^{2} - 512

= \frac{x ^{6} ( x ^{6} - 24 x ^{4} + 192 x ^{2} - 512 )}{3}

Expand

x^{6} (x^{6} - 24 x^{4} + 192 x^{2} - 512) : x^{12} - 24 x^{10} + 192 x^{8} - 512 x^{6}

= \frac{x ^{12} - 24 x ^{10} + 192 x ^{8} - 512 x ^{6}}{3}

Apply the fraction rule:

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

\frac{x ^{12} - 24 x ^{10} + 192 x ^{8} - 512 x ^{6}}{3} = \frac{x ^{12}}{3} - \frac{24 x ^{10}}{3} + \frac{192 x ^{8}}{3} - \frac{512 x ^{6}}{3}

= \frac{x ^{12}}{3} - \frac{24 x ^{10}}{3} + \frac{192 x ^{8}}{3} - \frac{512 x ^{6}}{3}

Divide the numbers:

\frac{24}{3} = 8

= \frac{x ^{12}}{3} - 8 x^{10} + \frac{192 x ^{8}}{3} - \frac{512 x ^{6}}{3}

Divide the numbers:

\frac{192}{3} = 64

= \frac{x ^{12}}{3} - 8 x^{10} + 64 x^{8} - \frac{512 x ^{6}}{3}

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What is expand (x^6(x^2-8)^3)/3 ?
The solution to expand (x^6(x^2-8)^3)/3 is (x^{12})/3-8x^{10}+64x^8-(512x^6)/3