Algebra Examples

$16 x^{2} + 24 x$

Factor out the $16$

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

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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Multiply the numerator by the reciprocal of the denominator.

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

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

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

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

Multiply $2$ by $2$ .

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

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

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

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

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

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

$\frac{9}{16}$

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

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

Simplify.

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Apply the distributive property.

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

Simplify.

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Cancel the common factor of $2$ .

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Factor $2$ out of $16$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Multiply $3$ by $8$ .

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

Cancel the common factor of $16$ .

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Cancel the common factor.

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

Rewrite the expression.

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

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