Precalculus Examples

$16 - {(x + 2)}^{2}$

Step 1

Simplify each term.

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Step 1.1

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

$16 - ((x + 2) (x + 2))$

Step 1.2

Expand $(x + 2) (x + 2)$ using the FOIL Method.

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Step 1.2.1

Apply the distributive property.

$16 - (x (x + 2) + 2 (x + 2))$

Step 1.2.2

Apply the distributive property.

$16 - (x \cdot x + x \cdot 2 + 2 (x + 2))$

Step 1.2.3

Apply the distributive property.

$16 - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2)$

$16 - (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2)$

Step 1.3

Simplify and combine like terms.

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Step 1.3.1

Simplify each term.

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Step 1.3.1.1

Multiply $x$ by $x$ .

$16 - (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2)$

Step 1.3.1.2

Move $2$ to the left of $x$ .

$16 - (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2)$

Step 1.3.1.3

Multiply $2$ by $2$ .

$16 - (x^{2} + 2 x + 2 x + 4)$

$16 - (x^{2} + 2 x + 2 x + 4)$

Step 1.3.2

Add $2 x$ and $2 x$ .

$16 - (x^{2} + 4 x + 4)$

$16 - (x^{2} + 4 x + 4)$

Step 1.4

Apply the distributive property.

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

Step 1.5

Simplify.

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Step 1.5.1

Multiply $4$ by $- 1$ .

$16 - x^{2} - 4 x - 1 \cdot 4$

Step 1.5.2

Multiply $- 1$ by $4$ .

$16 - x^{2} - 4 x - 4$

$16 - x^{2} - 4 x - 4$

$16 - x^{2} - 4 x - 4$

Step 2

Subtract $4$ from $16$ .

$- x^{2} - 4 x + 12$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$