What is expand ((3x+4)x^2(x-1)^2)/4 ?

The solution to expand ((3x+4)x^2(x-1)^2)/4 is (3x^5)/4-(x^4)/2-(5x^3)/4+x^2

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expand ((3x+4)x^2(x-1)^2)/4

expand

\frac{( 3 x + 4 ) x ^{2} ( x - 1 ) ^{2}}{4}

\frac{3 x ^{5}}{4} - \frac{x ^{4}}{2} - \frac{5 x ^{3}}{4} + x^{2}

Solution steps

\frac{( 3 x + 4 ) x ^{2} ( x - 1 ) ^{2}}{4}

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

= \frac{x ^{2} ( 3 x + 4 ) ( x ^{2} - 2 x + 1 )}{4}

Expand

(3 x + 4) x^{2} (x^{2} - 2 x + 1) : 3 x^{5} - 2 x^{4} - 5 x^{3} + 4 x^{2}

= \frac{3 x ^{5} - 2 x ^{4} - 5 x ^{3} + 4 x ^{2}}{4}

Apply the fraction rule:

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

\frac{3 x ^{5} - 2 x ^{4} - 5 x ^{3} + 4 x ^{2}}{4} = \frac{3 x ^{5}}{4} - \frac{2 x ^{4}}{4} - \frac{5 x ^{3}}{4} + \frac{4 x ^{2}}{4}

= \frac{3 x ^{5}}{4} - \frac{2 x ^{4}}{4} - \frac{5 x ^{3}}{4} + \frac{4 x ^{2}}{4}

Cancel

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

= \frac{3 x ^{5}}{4} - \frac{x ^{4}}{2} - \frac{5 x ^{3}}{4} + \frac{4 x ^{2}}{4}

Divide the numbers:

\frac{4}{4} = 1

= \frac{3 x ^{5}}{4} - \frac{x ^{4}}{2} - \frac{5 x ^{3}}{4} + x^{2}

\frac{x ( x - 3 ) ( x - 4 )}{4}

\frac{1}{2} (y - \frac{1}{2} sin (2 y))

\frac{2 n + 1}{2 ( n + 1 ) ^{2}}

\frac{2 ( 2 z - 5 )}{45}

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

What is expand ((3x+4)x^2(x-1)^2)/4 ?
The solution to expand ((3x+4)x^2(x-1)^2)/4 is (3x^5)/4-(x^4)/2-(5x^3)/4+x^2