Find the Perfect Square Trinomial 4x^2-32x+c

$4 x^{2} - 32 x + c$

Step 1

Move $- 32 x$ .

$4 x^{2} + c - 32 x$

Step 2

Factor out the $4$

$4 (x^{2} - 8 x + \frac{c}{4})$

Step 3

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

Divide $8$ by $2$ .

${(- 1 \cdot 4)}^{2}$

Multiply $- 1$ by $4$ .

${(- 4)}^{2}$

Raise $- 4$ to the power of $2$ .

$16$

Step 4

Add $16$ to get the perfect square trinomial.

$4 (x^{2} - 8 x + \frac{c}{4} + 16)$

Step 5

Simplify.

Apply the distributive property.

$4 x^{2} + 4 (- 8 x) + 4 \frac{c}{4} + 4 \cdot 16$

Simplify.

Multiply $- 8$ by $4$ .

$4 x^{2} - 32 x + 4 \frac{c}{4} + 4 \cdot 16$

Cancel the common factor of $4$ .

Cancel the common factor.

$4 x^{2} - 32 x + 4 \frac{c}{4} + 4 \cdot 16$

Rewrite the expression.

$4 x^{2} - 32 x + c + 4 \cdot 16$

Multiply $4$ by $16$ .

$4 x^{2} - 32 x + c + 64$