Pre-Algebra Examples

$f (x) = 2 {(x + 2)}^{2} + 5$

Step 1

Rewrite the function as an equation.

$y = 2 {(x + 2)}^{2} + 5$

Step 2

Simplify $2 {(x + 2)}^{2} + 5$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

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

$y = 2 ((x + 2) (x + 2)) + 5$

Step 2.1.2

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

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Step 2.1.2.1

Apply the distributive property.

$y = 2 (x (x + 2) + 2 (x + 2)) + 5$

Step 2.1.2.2

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 2 + 2 (x + 2)) + 5$

Step 2.1.2.3

Apply the distributive property.

$y = 2 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) + 5$

$y = 2 (x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2) + 5$

Step 2.1.3

Simplify and combine like terms.

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Step 2.1.3.1

Simplify each term.

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Step 2.1.3.1.1

Multiply $x$ by $x$ .

$y = 2 (x^{2} + x \cdot 2 + 2 x + 2 \cdot 2) + 5$

Step 2.1.3.1.2

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

$y = 2 (x^{2} + 2 \cdot x + 2 x + 2 \cdot 2) + 5$

Step 2.1.3.1.3

Multiply $2$ by $2$ .

$y = 2 (x^{2} + 2 x + 2 x + 4) + 5$

$y = 2 (x^{2} + 2 x + 2 x + 4) + 5$

Step 2.1.3.2

Add $2 x$ and $2 x$ .

$y = 2 (x^{2} + 4 x + 4) + 5$

$y = 2 (x^{2} + 4 x + 4) + 5$

Step 2.1.4

Apply the distributive property.

$y = 2 x^{2} + 2 (4 x) + 2 \cdot 4 + 5$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $4$ by $2$ .

$y = 2 x^{2} + 8 x + 2 \cdot 4 + 5$

Step 2.1.5.2

Multiply $2$ by $4$ .

$y = 2 x^{2} + 8 x + 8 + 5$

$y = 2 x^{2} + 8 x + 8 + 5$

$y = 2 x^{2} + 8 x + 8 + 5$

Step 2.2

Add $8$ and $5$ .

$y = 2 x^{2} + 8 x + 13$

$y = 2 x^{2} + 8 x + 13$

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