What is expand ((x-5)^4)/4 ?

The solution to expand ((x-5)^4)/4 is (x^4)/4-5x^3+(75x^2)/2-125x+625/4

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expand ((x-5)^4)/4

expand

\frac{( x - 5 ) ^{4}}{4}

\frac{x ^{4}}{4} - 5 x^{3} + \frac{75 x ^{2}}{2} - 125 x + \frac{625}{4}

Solution steps

\frac{( x - 5 ) ^{4}}{4}

(x - 5)^{4} = x^{4} - 20 x^{3} + 150 x^{2} - 500 x + 625

= \frac{x ^{4} - 20 x ^{3} + 150 x ^{2} - 500 x + 625}{4}

Apply the fraction rule:

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

\frac{x ^{4} - 20 x ^{3} + 150 x ^{2} - 500 x + 625}{4} = \frac{x ^{4}}{4} - \frac{20 x ^{3}}{4} + \frac{150 x ^{2}}{4} - \frac{500 x}{4} + \frac{625}{4}

= \frac{x ^{4}}{4} - \frac{20 x ^{3}}{4} + \frac{150 x ^{2}}{4} - \frac{500 x}{4} + \frac{625}{4}

Divide the numbers:

\frac{20}{4} = 5

= \frac{x ^{4}}{4} - 5 x^{3} + \frac{150 x ^{2}}{4} - \frac{500 x}{4} + \frac{625}{4}

Cancel

\frac{150 x ^{2}}{4} : \frac{75 x ^{2}}{2}

= \frac{x ^{4}}{4} - 5 x^{3} + \frac{75 x ^{2}}{2} - \frac{500 x}{4} + \frac{625}{4}

Divide the numbers:

\frac{500}{4} = 125

= \frac{x ^{4}}{4} - 5 x^{3} + \frac{75 x ^{2}}{2} - 125 x + \frac{625}{4}

\frac{k ( k + 1 ) ( k + 2 )}{6}

(y - 2 x) d x

j (z - e^{T (j - 1)}) (z - e^{T (- j - 1)})

\frac{( x - 5 )}{x ( x - 7 )}

- 3 (2 x + 5 y = 15)

What is expand ((x-5)^4)/4 ?
The solution to expand ((x-5)^4)/4 is (x^4)/4-5x^3+(75x^2)/2-125x+625/4