What is expand (x(x-2)^2(x+4))/(10) ?

The solution to expand (x(x-2)^2(x+4))/(10) is (x^4}{10}-\frac{6x^2)/5+(8x)/5

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expand (x(x-2)^2(x+4))/(10)

expand

\frac{x ( x - 2 ) ^{2} ( x + 4 )}{10}

\frac{x ^{4}}{10} - \frac{6 x ^{2}}{5} + \frac{8 x}{5}

Solution steps

\frac{x ( x - 2 ) ^{2} ( x + 4 )}{10}

(x - 2)^{2} = x^{2} - 4 x + 4

= \frac{x ( x ^{2} - 4 x + 4 ) ( x + 4 )}{10}

Expand

x (x^{2} - 4 x + 4) (x + 4) : x^{4} - 12 x^{2} + 16 x

= \frac{x ^{4} - 12 x ^{2} + 16 x}{10}

Apply the fraction rule:

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

\frac{x ^{4} - 12 x ^{2} + 16 x}{10} = \frac{x ^{4}}{10} - \frac{12 x ^{2}}{10} + \frac{16 x}{10}

= \frac{x ^{4}}{10} - \frac{12 x ^{2}}{10} + \frac{16 x}{10}

Cancel

\frac{12 x ^{2}}{10} : \frac{6 x ^{2}}{5}

= \frac{x ^{4}}{10} - \frac{6 x ^{2}}{5} + \frac{16 x}{10}

Cancel

\frac{16 x}{10} : \frac{8 x}{5}

= \frac{x ^{4}}{10} - \frac{6 x ^{2}}{5} + \frac{8 x}{5}

\frac{16 x y}{( x ^{2} + y ^{2} ) ^{2}}

\frac{3 z ^{3}}{( z - 0.5 ) ^{4}}

\frac{( x + h ) ^{2} + 2 ( x + h )}{h}

\frac{d y}{( y - 2 ) ( y + 2 )}

(x = 10,) (y = - 10)

What is expand (x(x-2)^2(x+4))/(10) ?
The solution to expand (x(x-2)^2(x+4))/(10) is (x^4}{10}-\frac{6x^2)/5+(8x)/5