Basic Math Examples

$- \frac{1}{3} {(x + 4)}^{2}$

Step 1

Rewrite ${(x + 4)}^{2}$ as $(x + 4) (x + 4)$ .

$- \frac{1}{3} \cdot ((x + 4) (x + 4))$

Step 2

Expand $(x + 4) (x + 4)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- \frac{1}{3} \cdot (x (x + 4) + 4 (x + 4))$

Step 2.2

Apply the distributive property.

$- \frac{1}{3} \cdot (x \cdot x + x \cdot 4 + 4 (x + 4))$

Step 2.3

Apply the distributive property.

$- \frac{1}{3} \cdot (x \cdot x + x \cdot 4 + 4 x + 4 \cdot 4)$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

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

Step 3.1.2

Move $4$ to the left of $x$ .

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

Step 3.1.3

Multiply $4$ by $4$ .

$- \frac{1}{3} \cdot (x^{2} + 4 x + 4 x + 16)$

Step 3.2

Add $4 x$ and $4 x$ .

$- \frac{1}{3} \cdot (x^{2} + 8 x + 16)$

Step 4

Apply the distributive property.

$- \frac{1}{3} x^{2} - \frac{1}{3} (8 x) - \frac{1}{3} \cdot 16$

Step 5

Simplify.

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Step 5.1

Combine $x^{2}$ and $\frac{1}{3}$ .

$- \frac{x^{2}}{3} - \frac{1}{3} (8 x) - \frac{1}{3} \cdot 16$

Step 5.2

Multiply $- \frac{1}{3} (8 x)$ .

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Step 5.2.1

Multiply $8$ by $- 1$ .

$- \frac{x^{2}}{3} - 8 (\frac{1}{3}) x - \frac{1}{3} \cdot 16$

Step 5.2.2

Combine $- 8$ and $\frac{1}{3}$ .

$- \frac{x^{2}}{3} + \frac{- 8}{3} x - \frac{1}{3} \cdot 16$

Step 5.2.3

Combine $\frac{- 8}{3}$ and $x$ .

$- \frac{x^{2}}{3} + \frac{- 8 x}{3} - \frac{1}{3} \cdot 16$

Step 5.3

Multiply $- \frac{1}{3} \cdot 16$ .

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Step 5.3.1

Multiply $16$ by $- 1$ .

$- \frac{x^{2}}{3} + \frac{- 8 x}{3} - 16 (\frac{1}{3})$

Step 5.3.2

Combine $- 16$ and $\frac{1}{3}$ .

$- \frac{x^{2}}{3} + \frac{- 8 x}{3} + \frac{- 16}{3}$

Step 6

Simplify each term.

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Step 6.1

Move the negative in front of the fraction.

$- \frac{x^{2}}{3} - \frac{8 x}{3} + \frac{- 16}{3}$

Step 6.2

Move the negative in front of the fraction.

$- \frac{x^{2}}{3} - \frac{8 x}{3} - \frac{16}{3}$