What is expand+(x(-x+3)^2)/6 ?

The solution to expand+(x(-x+3)^2)/6 is (x^3)/6-x^2+(3x)/2

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expand+(x(-x+3)^2)/6

expand

+ \frac{x ( - x + 3 ) ^{2}}{6}

\frac{x ^{3}}{6} - x^{2} + \frac{3 x}{2}

Solution steps

\frac{x ( - x + 3 ) ^{2}}{6}

(- x + 3)^{2} = x^{2} - 6 x + 9

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

Expand

x (x^{2} - 6 x + 9) : x^{3} - 6 x^{2} + 9 x

= \frac{x ^{3} - 6 x ^{2} + 9 x}{6}

Apply the fraction rule:

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

\frac{x ^{3} - 6 x ^{2} + 9 x}{6} = \frac{x ^{3}}{6} - \frac{6 x ^{2}}{6} + \frac{9 x}{6}

= \frac{x ^{3}}{6} - \frac{6 x ^{2}}{6} + \frac{9 x}{6}

Divide the numbers:

\frac{6}{6} = 1

= \frac{x ^{3}}{6} - x^{2} + \frac{9 x}{6}

Cancel

\frac{9 x}{6} : \frac{3 x}{2}

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

(1.01)^{3}

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

(t + δ t)^{2}

3 (3 x^{2} + 6 x - 1)^{2}

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

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