Find the Perfect Square Trinomial p^2-5p

$p^{2} - 5 p$

Step 1

To find the $c$ value $c = {(\frac{b}{2})}^{2}$ , divide the coefficient of $p$ 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 $- \frac{5}{2}$ .

${(- 1)}^{2} {(\frac{5}{2})}^{2}$

Apply the product rule to $\frac{5}{2}$ .

${(- 1)}^{2} \frac{5^{2}}{2^{2}}$

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

$1 \frac{5^{2}}{2^{2}}$

Multiply $\frac{5^{2}}{2^{2}}$ by $1$ .

$\frac{5^{2}}{2^{2}}$

Raise $5$ to the power of $2$ .

$\frac{25}{2^{2}}$

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

$\frac{25}{4}$

Step 2

Add $\frac{25}{4}$ to get the perfect square trinomial.

$p^{2} - 5 p + \frac{25}{4}$