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

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

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

expand

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

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

Solution steps

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

Apply the fraction rule:

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

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

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

Divide the numbers:

\frac{4}{4} = 1

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

Cancel

\frac{6 a ^{2} x ^{2}}{4} : \frac{3 a ^{2} x ^{2}}{2}

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

Divide the numbers:

\frac{4}{4} = 1

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

4 (3 cos (t) + 1) - (3 sin (t) + 3)^{2} sin (3 cos (t) + 1)

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

(2 \times (- 5) γ)^{3}

y \cdot 6 sin (3 x - 2 y) (x + 3 y)^{2} + x \cdot (- 9) sin (3 x - 2 y)

C_{4} (- 27 e^{- 3 x} x + 27 e^{- 3 x})

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