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

The solution to expand ((x-2)(x+4)^2)/((x+2)^3) is (x^3+6x^2-32)/(x^3+6x^2+12x+8)

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

expand

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

\frac{x ^{3} + 6 x ^{2} - 32}{x ^{3} + 6 x ^{2} + 12 x + 8}

Solution steps

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

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

= \frac{( x - 2 ) ( x + 4 ) ^{2}}{x ^{3} + 6 x ^{2} + 12 x + 8}

(x + 4)^{2} = x^{2} + 8 x + 16

= \frac{( x - 2 ) ( x ^{2} + 8 x + 16 )}{x ^{3} + 6 x ^{2} + 12 x + 8}

Expand

(x - 2) (x^{2} + 8 x + 16) : x^{3} + 6 x^{2} - 32

= \frac{x ^{3} + 6 x ^{2} - 32}{x ^{3} + 6 x ^{2} + 12 x + 8}

\frac{1}{( x + a ) ^{2}}

\frac{4}{( s - 1 ) ^{3}}

\frac{- 2 x ^{2} - 4 x + 9}{( 2 x ^{2} - 5 x + 4 ) ^{2}}

\frac{1}{x + 10} + \frac{1}{x + 5} + \frac{1}{x + 1} - \frac{1}{x + 2}

e^{2 (x + 1)}

What is expand ((x-2)(x+4)^2)/((x+2)^3) ?
The solution to expand ((x-2)(x+4)^2)/((x+2)^3) is (x^3+6x^2-32)/(x^3+6x^2+12x+8)