What is expand ((2x+4)^3)/3 ?

The solution to expand ((2x+4)^3)/3 is (8x^3)/3+16x^2+32x+64/3

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expand ((2x+4)^3)/3

expand

\frac{( 2 x + 4 ) ^{3}}{3}

\frac{8 x ^{3}}{3} + 16 x^{2} + 32 x + \frac{64}{3}

Solution steps

\frac{( 2 x + 4 ) ^{3}}{3}

(2 x + 4)^{3} = 8 x^{3} + 48 x^{2} + 96 x + 64

= \frac{8 x ^{3} + 48 x ^{2} + 96 x + 64}{3}

Apply the fraction rule:

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

\frac{8 x ^{3} + 48 x ^{2} + 96 x + 64}{3} = \frac{8 x ^{3}}{3} + \frac{48 x ^{2}}{3} + \frac{96 x}{3} + \frac{64}{3}

= \frac{8 x ^{3}}{3} + \frac{48 x ^{2}}{3} + \frac{96 x}{3} + \frac{64}{3}

Divide the numbers:

\frac{48}{3} = 16

= \frac{8 x ^{3}}{3} + 16 x^{2} + \frac{96 x}{3} + \frac{64}{3}

Divide the numbers:

\frac{96}{3} = 32

= \frac{8 x ^{3}}{3} + 16 x^{2} + 32 x + \frac{64}{3}

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What is expand ((2x+4)^3)/3 ?
The solution to expand ((2x+4)^3)/3 is (8x^3)/3+16x^2+32x+64/3