What is expand ((a-1)^4)/4 ?

The solution to expand ((a-1)^4)/4 is (a^4)/4-a^3+(3a^2)/2-a+1/4

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expand ((a-1)^4)/4

expand

\frac{( a - 1 ) ^{4}}{4}

\frac{a ^{4}}{4} - a^{3} + \frac{3 a ^{2}}{2} - a + \frac{1}{4}

Solution steps

\frac{( a - 1 ) ^{4}}{4}

(a - 1)^{4} = a^{4} - 4 a^{3} + 6 a^{2} - 4 a + 1

= \frac{a ^{4} - 4 a ^{3} + 6 a ^{2} - 4 a + 1}{4}

Apply the fraction rule:

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

\frac{a ^{4} - 4 a ^{3} + 6 a ^{2} - 4 a + 1}{4} = \frac{a ^{4}}{4} - \frac{4 a ^{3}}{4} + \frac{6 a ^{2}}{4} - \frac{4 a}{4} + \frac{1}{4}

= \frac{a ^{4}}{4} - \frac{4 a ^{3}}{4} + \frac{6 a ^{2}}{4} - \frac{4 a}{4} + \frac{1}{4}

Divide the numbers:

\frac{4}{4} = 1

= \frac{a ^{4}}{4} - a^{3} + \frac{6 a ^{2}}{4} - \frac{4 a}{4} + \frac{1}{4}

Cancel

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

= \frac{a ^{4}}{4} - a^{3} + \frac{3 a ^{2}}{2} - \frac{4 a}{4} + \frac{1}{4}

Divide the numbers:

\frac{4}{4} = 1

= \frac{a ^{4}}{4} - a^{3} + \frac{3 a ^{2}}{2} - a + \frac{1}{4}

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

\frac{3}{( 2 s + 4 ) ^{2}}

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

x (4 - x) e^{0.5 x} - 2

\frac{4}{9 ( 18 x + 81 y )}

What is expand ((a-1)^4)/4 ?
The solution to expand ((a-1)^4)/4 is (a^4)/4-a^3+(3a^2)/2-a+1/4