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

Remove parentheses:

(a) = a, - (- a) = a

= - \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}

sec (x) (1 + x tan (x))

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

, x^{2} (x + 2)

\frac{π ( 2 ln ( 2 ) + 1 )}{2}

1 + tan^{2} (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