Algebra Examples

16 x^{2} + 24 x

$16 x^{2} + 24 x$

Step 1

Factor out the

16

$16$

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

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

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

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

Step 2.2

Multiply

\frac{3}{2} \cdot \frac{1}{2}

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

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Step 2.2.1

Multiply

\frac{3}{2}

$\frac{3}{2}$ by

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 2.2.2

Multiply

2

$2$ by

2

$2$ .

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

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

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

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

Step 2.3

Apply the product rule to

\frac{3}{4}

$\frac{3}{4}$ .

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

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

Step 2.4

Raise

3

$3$ to the power of

2

$2$ .

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

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

Step 2.5

Raise

4

$4$ to the power of

2

$2$ .

\frac{9}{16}

$\frac{9}{16}$

\frac{9}{16}

$\frac{9}{16}$

Step 3

Add

\frac{9}{16}

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

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

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

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})

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

Step 4.2

Simplify.

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Step 4.2.1

Cancel the common factor of

2

$2$ .

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Step 4.2.1.1

Factor

2

$2$ out of

16

$16$ .

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

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

Step 4.2.1.3

Rewrite the expression.

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

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

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

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

Step 4.2.2

Multiply

3

$3$ by

8

$8$ .

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

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

Step 4.2.3

Cancel the common factor of

16

$16$ .

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Step 4.2.3.1

Cancel the common factor.

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

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

Step 4.2.3.2

Rewrite the expression.

16 x^{2} + 24 x + 9

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

16 x^{2} + 24 x + 9

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

16 x^{2} + 24 x + 9

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

16 x^{2} + 24 x + 9

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

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