What is expand (x^2(x+1)^2)/4 ?

The solution to expand (x^2(x+1)^2)/4 is (x^4)/4+(x^3)/2+(x^2)/4

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expand (x^2(x+1)^2)/4

expand

\frac{x ^{2} ( x + 1 ) ^{2}}{4}

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

Solution steps

\frac{x ^{2} ( x + 1 ) ^{2}}{4}

(x + 1)^{2} = x^{2} + 2 x + 1

= \frac{x ^{2} ( x ^{2} + 2 x + 1 )}{4}

Expand

x^{2} (x^{2} + 2 x + 1) : x^{4} + 2 x^{3} + x^{2}

= \frac{x ^{4} + 2 x ^{3} + x ^{2}}{4}

Apply the fraction rule:

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

\frac{x ^{4} + 2 x ^{3} + x ^{2}}{4} = \frac{x ^{4}}{4} + \frac{2 x ^{3}}{4} + \frac{x ^{2}}{4}

= \frac{x ^{4}}{4} + \frac{2 x ^{3}}{4} + \frac{x ^{2}}{4}

Cancel

\frac{2 x ^{3}}{4} : \frac{x ^{3}}{2}

= \frac{x ^{4}}{4} + \frac{x ^{3}}{2} + \frac{x ^{2}}{4}

\frac{10 x ( - 5 x ^{3} + y ^{3} )}{y ^{5}}

\frac{- s e ^{- π s} + s ( s ^{2} + 1 )}{( s ^{2} + 1 ) ( s ^{2} + 4 )}

\frac{d x}{x ( 4 - x )}

\frac{d ^{2}}{d x ^{2}} ((y) (x^{2} + y^{2} - 6 x - 8 y + 16))

(\frac{1}{x ^{2}} - 3 x)^{5}

What is expand (x^2(x+1)^2)/4 ?
The solution to expand (x^2(x+1)^2)/4 is (x^4)/4+(x^3)/2+(x^2)/4