Precalculus Examples

$4 x^{2} - 5 x$

Factor out the $4$

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

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.

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

Multiply $\frac{5}{4} \cdot \frac{1}{2}$ .

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Multiply $\frac{5}{4}$ and $\frac{1}{2}$ .

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

Multiply $4$ by $2$ .

${(- \frac{5}{8})}^{2}$

Use the power rule ${(a b)}^{n} = a^{n} b^{n}$ to distribute the exponent.

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Apply the product rule to $- \frac{5}{8}$ .

${(- 1)}^{2} {(\frac{5}{8})}^{2}$

Apply the product rule to $\frac{5}{8}$ .

${(- 1)}^{2} \frac{5^{2}}{8^{2}}$

Raise $- 1$ to the power of $2$ .

$1 \frac{5^{2}}{8^{2}}$

Multiply $\frac{5^{2}}{8^{2}}$ by $1$ .

$\frac{5^{2}}{8^{2}}$

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

$\frac{25}{8^{2}}$

Raise $8$ to the power of $2$ .

$\frac{25}{64}$

Add $\frac{25}{64}$ to get the perfect square trinomial.

$4 (x^{2} - \frac{5 x}{4} + \frac{25}{64})$

Simplify.

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Apply the distributive property.

$4 x^{2} + 4 (- \frac{5 x}{4}) + 4 (\frac{25}{64})$

Simplify.

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Cancel the common factor of $4$ .

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Move the leading negative in $- \frac{5 x}{4}$ into the numerator.

$4 x^{2} + 4 \frac{- 5 x}{4} + 4 (\frac{25}{64})$

Write $4$ as a fraction with denominator $1$ .

$4 x^{2} + \frac{4}{1} \cdot \frac{- 5 x}{4} + 4 (\frac{25}{64})$

Factor out the greatest common factor $4$ .

$4 x^{2} + \frac{4 \cdot 1}{1} \cdot \frac{- 5 x}{4 \cdot 1} + 4 (\frac{25}{64})$

Cancel the common factor.

$4 x^{2} + \frac{4 \cdot 1}{1} \cdot \frac{- 5 x}{4 \cdot 1} + 4 (\frac{25}{64})$

Rewrite the expression.

$4 x^{2} + \frac{1}{1} \cdot \frac{- 5 x}{1} + 4 (\frac{25}{64})$

Simplify.

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Multiply $\frac{1}{1}$ and $\frac{- 5 x}{1}$ .

$4 x^{2} + \frac{- 5 x}{1} + 4 (\frac{25}{64})$

Divide $- 5 x$ by $1$ .

$4 x^{2} - 5 x + 4 (\frac{25}{64})$

Cancel the common factor of $4$ .

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Write $4$ as a fraction with denominator $1$ .

$4 x^{2} - 5 x + \frac{4}{1} \cdot \frac{25}{64}$

Factor out the greatest common factor $4$ .

$4 x^{2} - 5 x + \frac{4 \cdot 1}{1} \cdot \frac{25}{4 \cdot 16}$

Cancel the common factor.

$4 x^{2} - 5 x + \frac{4 \cdot 1}{1} \cdot \frac{25}{4 \cdot 16}$

Rewrite the expression.

$4 x^{2} - 5 x + \frac{1}{1} \cdot \frac{25}{16}$

Multiply $\frac{1}{1}$ and $\frac{25}{16}$ .

$4 x^{2} - 5 x + \frac{25}{16}$

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