Precalculus Examples Algebra Concepts and Expressions

Find the Perfect Square Trinomial

$16 x^{2} + 24 x$

Step 1

Factor out the $16$

$16 (x^{2} + \frac{3 x}{2})$

Step 2

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

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

${(\frac{3}{2} \cdot \frac{1}{2})}^{2}$

Step 2.2

Multiply $\frac{3}{2} \cdot \frac{1}{2}$ .

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Step 2.2.1

Multiply $\frac{3}{2}$ by $\frac{1}{2}$ .

${(\frac{3}{2 \cdot 2})}^{2}$

Step 2.2.2

Multiply $2$ by $2$ .

${(\frac{3}{4})}^{2}$

Step 2.3

Apply the product rule to $\frac{3}{4}$ .

$\frac{3^{2}}{4^{2}}$

Step 2.4

Raise $3$ to the power of $2$ .

$\frac{9}{4^{2}}$

Step 2.5

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

$\frac{9}{16}$

Step 3

Add $\frac{9}{16}$ to get the perfect square trinomial.

$16 (x^{2} + \frac{3 x}{2} + \frac{9}{16})$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

$16 x^{2} + 16 \frac{3 x}{2} + 16 (\frac{9}{16})$

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of $2$ .

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Step 4.2.1.1

Factor $2$ out of $16$ .

$16 x^{2} + 2 (8) \frac{3 x}{2} + 16 (\frac{9}{16})$

Step 4.2.1.2

Cancel the common factor.

$16 x^{2} + 2 \cdot 8 \frac{3 x}{2} + 16 (\frac{9}{16})$

Step 4.2.1.3

Rewrite the expression.

$16 x^{2} + 8 (3 x) + 16 (\frac{9}{16})$

Step 4.2.2

Multiply $3$ by $8$ .

$16 x^{2} + 24 x + 16 (\frac{9}{16})$

Step 4.2.3

Cancel the common factor of $16$ .

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Step 4.2.3.1

Cancel the common factor.

$16 x^{2} + 24 x + 16 (\frac{9}{16})$

Step 4.2.3.2

Rewrite the expression.

$16 x^{2} + 24 x + 9$

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