What is expand (x*(a-x)^3)/3 ?

The solution to expand (x*(a-x)^3)/3 is (a^3x)/3-a^2x^2+ax^3-(x^4)/3

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expand (x*(a-x)^3)/3

expand

\frac{x \cdot ( a - x ) ^{3}}{3}

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

Solution steps

\frac{x ( a - x ) ^{3}}{3}

(a - x)^{3} = a^{3} - 3 a^{2} x + 3 a x^{2} - x^{3}

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

Expand

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

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{3}{3} = 1

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

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

e^{4 x} (4 b + c + x c)

[\frac{4}{( 2 x - 1 ) ^{2}}]

\frac{5 ( 20 + 106 )}{49}

(f \circ g) (x^{2} + 3 x - 3) (3 x - 8)

What is expand (x*(a-x)^3)/3 ?
The solution to expand (x*(a-x)^3)/3 is (a^3x)/3-a^2x^2+ax^3-(x^4)/3