What is expand ((x+2)^3(9x-2))/(12) ?

The solution to expand ((x+2)^3(9x-2))/(12) is (3x^4)/4+(13x^3)/3+8x^2+4x-4/3

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expand ((x+2)^3(9x-2))/(12)

expand

\frac{( x + 2 ) ^{3} ( 9 x - 2 )}{12}

\frac{3 x ^{4}}{4} + \frac{13 x ^{3}}{3} + 8 x^{2} + 4 x - \frac{4}{3}

Solution steps

\frac{( x + 2 ) ^{3} ( 9 x - 2 )}{12}

(x + 2)^{3} = x^{3} + 6 x^{2} + 12 x + 8

= \frac{( x ^{3} + 6 x ^{2} + 12 x + 8 ) ( 9 x - 2 )}{12}

Expand

(x^{3} + 6 x^{2} + 12 x + 8) (9 x - 2) : 9 x^{4} + 52 x^{3} + 96 x^{2} + 48 x - 16

= \frac{9 x ^{4} + 52 x ^{3} + 96 x ^{2} + 48 x - 16}{12}

Apply the fraction rule:

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

\frac{9 x ^{4} + 52 x ^{3} + 96 x ^{2} + 48 x - 16}{12} = \frac{9 x ^{4}}{12} + \frac{52 x ^{3}}{12} + \frac{96 x ^{2}}{12} + \frac{48 x}{12} - \frac{16}{12}

= \frac{9 x ^{4}}{12} + \frac{52 x ^{3}}{12} + \frac{96 x ^{2}}{12} + \frac{48 x}{12} - \frac{16}{12}

\frac{9 x ^{4}}{12} = \frac{3 x ^{4}}{4}

\frac{52 x ^{3}}{12} = \frac{13 x ^{3}}{3}

\frac{96 x ^{2}}{12} = 8 x^{2}

\frac{48 x}{12} = 4 x

\frac{16}{12} = \frac{4}{3}

= \frac{3 x ^{4}}{4} + \frac{13 x ^{3}}{3} + 8 x^{2} + 4 x - \frac{4}{3}

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

(t - a) (H (t - a) - H (t - b))

\frac{( 8 - x )}{( x + 2 ) ^{2}}

x^{2} y^{''} (x) + x (x + 2) y^{'} (x) - (x + 2) y

What is expand ((x+2)^3(9x-2))/(12) ?
The solution to expand ((x+2)^3(9x-2))/(12) is (3x^4)/4+(13x^3)/3+8x^2+4x-4/3