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

The solution to expand (3x(a-x)^4)/4 is (3a^4x)/4-3a^3x^2+(9a^2x^3)/2-3ax^4+(3x^5)/4

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expand (3x(a-x)^4)/4

expand

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

\frac{3 a ^{4} x}{4} - 3 a^{3} x^{2} + \frac{9 a ^{2} x ^{3}}{2} - 3 a x^{4} + \frac{3 x ^{5}}{4}

Solution steps

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

(a - x)^{4} = a^{4} - 4 a^{3} x + 6 a^{2} x^{2} - 4 a x^{3} + x^{4}

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

Expand

3 x (a^{4} - 4 a^{3} x + 6 a^{2} x^{2} - 4 a x^{3} + x^{4}) : 3 a^{4} x - 12 a^{3} x^{2} + 18 a^{2} x^{3} - 12 a x^{4} + 3 x^{5}

= \frac{3 a ^{4} x - 12 a ^{3} x ^{2} + 18 a ^{2} x ^{3} - 12 a x ^{4} + 3 x ^{5}}{4}

Apply the fraction rule:

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

\frac{3 a ^{4} x - 12 a ^{3} x ^{2} + 18 a ^{2} x ^{3} - 12 a x ^{4} + 3 x ^{5}}{4} = \frac{3 a ^{4} x}{4} - \frac{12 a ^{3} x ^{2}}{4} + \frac{18 a ^{2} x ^{3}}{4} - \frac{12 a x ^{4}}{4} + \frac{3 x ^{5}}{4}

= \frac{3 a ^{4} x}{4} - \frac{12 a ^{3} x ^{2}}{4} + \frac{18 a ^{2} x ^{3}}{4} - \frac{12 a x ^{4}}{4} + \frac{3 x ^{5}}{4}

Divide the numbers:

\frac{12}{4} = 3

= \frac{3 a ^{4} x}{4} - 3 a^{3} x^{2} + \frac{18 a ^{2} x ^{3}}{4} - \frac{12 a x ^{4}}{4} + \frac{3 x ^{5}}{4}

Cancel

\frac{18 a ^{2} x ^{3}}{4} : \frac{9 a ^{2} x ^{3}}{2}

= \frac{3 a ^{4} x}{4} - 3 a^{3} x^{2} + \frac{9 a ^{2} x ^{3}}{2} - \frac{12 a x ^{4}}{4} + \frac{3 x ^{5}}{4}

Divide the numbers:

\frac{12}{4} = 3

= \frac{3 a ^{4} x}{4} - 3 a^{3} x^{2} + \frac{9 a ^{2} x ^{3}}{2} - 3 a x^{4} + \frac{3 x ^{5}}{4}

4 x π (6 - x)^{2}

\frac{- ( - 2 ) ( 2 ( - 2 ) ^{2} + 3 ( - 2 ) - 12 )}{3}

\frac{2 ( 2 x - T )}{T}

\frac{1}{r ( n - r )}

\frac{d}{d t} ((r (t)) (2 sin (t) - e^{- t}))

What is expand (3x(a-x)^4)/4 ?
The solution to expand (3x(a-x)^4)/4 is (3a^4x)/4-3a^3x^2+(9a^2x^3)/2-3ax^4+(3x^5)/4