Algebra Examples

$16 x^{2} + 23 x$

Factor out the $16$

$16 (x^{2} + \frac{23 x}{16})$

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.

${(\frac{23}{16} \cdot \frac{1}{2})}^{2}$

Multiply $\frac{23}{16} \cdot \frac{1}{2}$ .

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Multiply $\frac{23}{16}$ and $\frac{1}{2}$ .

${(\frac{23}{16 \cdot 2})}^{2}$

Multiply $16$ by $2$ .

${(\frac{23}{32})}^{2}$

Apply the product rule to $\frac{23}{32}$ .

$\frac{23^{2}}{32^{2}}$

Raise $23$ to the power of $2$ .

$\frac{529}{32^{2}}$

Raise $32$ to the power of $2$ .

$\frac{529}{1024}$

Add $\frac{529}{1024}$ to get the perfect square trinomial.

$16 (x^{2} + \frac{23 x}{16} + \frac{529}{1024})$

Simplify.

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Apply the distributive property.

$16 x^{2} + 16 \frac{23 x}{16} + 16 (\frac{529}{1024})$

Simplify.

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Cancel the common factor of $16$ .

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Write $16$ as a fraction with denominator $1$ .

$16 x^{2} + \frac{16}{1} \cdot \frac{23 x}{16} + 16 (\frac{529}{1024})$

Factor out the greatest common factor $16$ .

$16 x^{2} + \frac{16 \cdot 1}{1} \cdot \frac{23 x}{16 \cdot 1} + 16 (\frac{529}{1024})$

Cancel the common factor.

$16 x^{2} + \frac{16 \cdot 1}{1} \cdot \frac{23 x}{16 \cdot 1} + 16 (\frac{529}{1024})$

Rewrite the expression.

$16 x^{2} + \frac{1}{1} \cdot \frac{23 x}{1} + 16 (\frac{529}{1024})$

Simplify.

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Multiply $\frac{1}{1}$ and $\frac{23 x}{1}$ .

$16 x^{2} + \frac{23 x}{1} + 16 (\frac{529}{1024})$

Divide $23 x$ by $1$ .

$16 x^{2} + 23 x + 16 (\frac{529}{1024})$

Cancel the common factor of $16$ .

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Write $16$ as a fraction with denominator $1$ .

$16 x^{2} + 23 x + \frac{16}{1} \cdot \frac{529}{1024}$

Factor out the greatest common factor $16$ .

$16 x^{2} + 23 x + \frac{16 \cdot 1}{1} \cdot \frac{529}{16 \cdot 64}$

Cancel the common factor.

$16 x^{2} + 23 x + \frac{16 \cdot 1}{1} \cdot \frac{529}{16 \cdot 64}$

Rewrite the expression.

$16 x^{2} + 23 x + \frac{1}{1} \cdot \frac{529}{64}$

Multiply $\frac{1}{1}$ and $\frac{529}{64}$ .

$16 x^{2} + 23 x + \frac{529}{64}$

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