Find the Perfect Square Trinomial 25x^2+20x

$25 x^{2} + 20 x$

Step 1

Factor out the $25$

$25 (x^{2} + \frac{4 x}{5})$

Step 2

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

Multiply the numerator by the reciprocal of the denominator.

${(\frac{4}{5} \cdot \frac{1}{2})}^{2}$

Cancel the common factor of $2$ .

Factor $2$ out of $4$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Simplify the expression.

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

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

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

$\frac{4}{5^{2}}$

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

$\frac{4}{25}$

Step 3

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

$25 (x^{2} + \frac{4 x}{5} + \frac{4}{25})$

Step 4

Simplify.

Apply the distributive property.

$25 x^{2} + 25 \frac{4 x}{5} + 25 (\frac{4}{25})$

Simplify.

Cancel the common factor of $5$ .

Factor $5$ out of $25$ .

$25 x^{2} + 5 (5) \frac{4 x}{5} + 25 (\frac{4}{25})$

Cancel the common factor.

$25 x^{2} + 5 \cdot 5 \frac{4 x}{5} + 25 (\frac{4}{25})$

Rewrite the expression.

$25 x^{2} + 5 (4 x) + 25 (\frac{4}{25})$

Multiply $4$ by $5$ .

$25 x^{2} + 20 x + 25 (\frac{4}{25})$

Cancel the common factor of $25$ .

Cancel the common factor.

$25 x^{2} + 20 x + 25 (\frac{4}{25})$

Rewrite the expression.

$25 x^{2} + 20 x + 4$