Find the Perfect Square Trinomial k^2-11k

$k^{2} - 11 k$

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $k$ by $2$ and square the result.

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

Apply the product rule to $- \frac{11}{2}$ .

${(- 1)}^{2} {(\frac{11}{2})}^{2}$

Apply the product rule to $\frac{11}{2}$ .

${(- 1)}^{2} \frac{11^{2}}{2^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{11^{2}}{2^{2}}$

Multiply $\frac{11^{2}}{2^{2}}$ by $1$ .

$\frac{11^{2}}{2^{2}}$

Raise $11$ to the power of $2$ .

$\frac{121}{2^{2}}$

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

$\frac{121}{4}$

Add $\frac{121}{4}$ to get the perfect square trinomial.

$k^{2} - 11 k + \frac{121}{4}$