Precalculus Examples

6 x^{2} + 8 x

$6 x^{2} + 8 x$

Step 1

Factor out the

6

$6$

6 (x^{2} + \frac{4 x}{3})

$6 (x^{2} + \frac{4 x}{3})$

Step 2

To find the

c

$c$ value

c = {(\frac{b}{2})}^{2}

$c = {(\frac{b}{2})}^{2}$ , divide the coefficient of

x

$x$ by

2

$2$ and square the result.

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Step 2.1

Multiply the numerator by the reciprocal of the denominator.

{(\frac{4}{3} \cdot \frac{1}{2})}^{2}

${(\frac{4}{3} \cdot \frac{1}{2})}^{2}$

Step 2.2

Cancel the common factor of

2

$2$ .

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Step 2.2.1

Factor

2

$2$ out of

4

$4$ .

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

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

Step 2.2.2

Cancel the common factor.

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

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

Step 2.2.3

Rewrite the expression.

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

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

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

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

Step 2.3

Simplify the expression.

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Step 2.3.1

Apply the product rule to

\frac{2}{3}

$\frac{2}{3}$ .

\frac{2^{2}}{3^{2}}

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

Step 2.3.2

Raise

2

$2$ to the power of

2

$2$ .

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

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

Step 2.3.3

Raise

3

$3$ to the power of

2

$2$ .

\frac{4}{9}

$\frac{4}{9}$

\frac{4}{9}

$\frac{4}{9}$

\frac{4}{9}

$\frac{4}{9}$

Step 3

Add

\frac{4}{9}

$\frac{4}{9}$ to get the perfect square trinomial.

6 (x^{2} + \frac{4 x}{3} + \frac{4}{9})

$6 (x^{2} + \frac{4 x}{3} + \frac{4}{9})$

Step 4

Simplify.

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Step 4.1

Apply the distributive property.

6 x^{2} + 6 \frac{4 x}{3} + 6 (\frac{4}{9})

$6 x^{2} + 6 \frac{4 x}{3} + 6 (\frac{4}{9})$

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of

3

$3$ .

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Step 4.2.1.1

Factor

3

$3$ out of

6

$6$ .

6 x^{2} + 3 (2) \frac{4 x}{3} + 6 (\frac{4}{9})

$6 x^{2} + 3 (2) \frac{4 x}{3} + 6 (\frac{4}{9})$

Step 4.2.1.2

Cancel the common factor.

6 x^{2} + 3 \cdot 2 \frac{4 x}{3} + 6 (\frac{4}{9})

$6 x^{2} + 3 \cdot 2 \frac{4 x}{3} + 6 (\frac{4}{9})$

Step 4.2.1.3

Rewrite the expression.

6 x^{2} + 2 (4 x) + 6 (\frac{4}{9})

$6 x^{2} + 2 (4 x) + 6 (\frac{4}{9})$

6 x^{2} + 2 (4 x) + 6 (\frac{4}{9})

$6 x^{2} + 2 (4 x) + 6 (\frac{4}{9})$

Step 4.2.2

Multiply

4

$4$ by

2

$2$ .

6 x^{2} + 8 x + 6 (\frac{4}{9})

$6 x^{2} + 8 x + 6 (\frac{4}{9})$

Step 4.2.3

Cancel the common factor of

3

$3$ .

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Step 4.2.3.1

Factor

3

$3$ out of

6

$6$ .

6 x^{2} + 8 x + 3 (2) \frac{4}{9}

$6 x^{2} + 8 x + 3 (2) \frac{4}{9}$

Step 4.2.3.2

Factor

3

$3$ out of

9

$9$ .

6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}

$6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}$

Step 4.2.3.3

Cancel the common factor.

6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}

$6 x^{2} + 8 x + 3 \cdot 2 \frac{4}{3 \cdot 3}$

Step 4.2.3.4

Rewrite the expression.

6 x^{2} + 8 x + 2 (\frac{4}{3})

$6 x^{2} + 8 x + 2 (\frac{4}{3})$

6 x^{2} + 8 x + 2 (\frac{4}{3})

$6 x^{2} + 8 x + 2 (\frac{4}{3})$

Step 4.2.4

Combine

2

$2$ and

\frac{4}{3}

$\frac{4}{3}$ .

6 x^{2} + 8 x + \frac{2 \cdot 4}{3}

$6 x^{2} + 8 x + \frac{2 \cdot 4}{3}$

Step 4.2.5

Multiply

2

$2$ by

4

$4$ .

6 x^{2} + 8 x + \frac{8}{3}

$6 x^{2} + 8 x + \frac{8}{3}$

6 x^{2} + 8 x + \frac{8}{3}

$6 x^{2} + 8 x + \frac{8}{3}$

6 x^{2} + 8 x + \frac{8}{3}

$6 x^{2} + 8 x + \frac{8}{3}$

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