Simplify ((n(n+1))/2)^2

${(\frac{n (n + 1)}{2})}^{2}$

Step 1

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

Apply the product rule to $\frac{n (n + 1)}{2}$ .

$\frac{{(n (n + 1))}^{2}}{2^{2}}$

Apply the product rule to $n (n + 1)$ .

$\frac{n^{2} {(n + 1)}^{2}}{2^{2}}$

Step 2

Raise $2$ to the power of $2$ .

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