What is expand (n^2(n-1)^2)/4 ?

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

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expand (n^2(n-1)^2)/4

expand

\frac{n ^{2} ( n - 1 ) ^{2}}{4}

\frac{n ^{4}}{4} - \frac{n ^{3}}{2} + \frac{n ^{2}}{4}

Solution steps

\frac{n ^{2} ( n - 1 ) ^{2}}{4}

(n - 1)^{2} = n^{2} - 2 n + 1

= \frac{n ^{2} ( n ^{2} - 2 n + 1 )}{4}

Expand

n^{2} (n^{2} - 2 n + 1) : n^{4} - 2 n^{3} + n^{2}

= \frac{n ^{4} - 2 n ^{3} + n ^{2}}{4}

Apply the fraction rule:

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

\frac{n ^{4} - 2 n ^{3} + n ^{2}}{4} = \frac{n ^{4}}{4} - \frac{2 n ^{3}}{4} + \frac{n ^{2}}{4}

= \frac{n ^{4}}{4} - \frac{2 n ^{3}}{4} + \frac{n ^{2}}{4}

Cancel

\frac{2 n ^{3}}{4} : \frac{n ^{3}}{2}

= \frac{n ^{4}}{4} - \frac{n ^{3}}{2} + \frac{n ^{2}}{4}

A (3, 4) y B (5, - 1)

p (- 3, 10) p (6, - 4)

((y + 1) e^{t} - x)^{2}

(1, - 2) \cdot (x, y)

\frac{3 ( k + 1 ) ( k + 2 )}{2}

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