Pre-Algebra Examples

$f (x) = {(x + 12)}^{2} + 30$

Step 1

Rewrite the function as an equation.

$y = {(x + 12)}^{2} + 30$

Step 2

Simplify ${(x + 12)}^{2} + 30$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x + 12)}^{2}$ as $(x + 12) (x + 12)$ .

$y = (x + 12) (x + 12) + 30$

Step 2.1.2

Expand $(x + 12) (x + 12)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$y = x (x + 12) + 12 (x + 12) + 30$

Step 2.1.2.2

Apply the distributive property.

$y = x \cdot x + x \cdot 12 + 12 (x + 12) + 30$

Step 2.1.2.3

Apply the distributive property.

$y = x \cdot x + x \cdot 12 + 12 x + 12 \cdot 12 + 30$

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 $x$ .

$y = x^{2} + x \cdot 12 + 12 x + 12 \cdot 12 + 30$

Step 2.1.3.1.2

Move $12$ to the left of $x$ .

$y = x^{2} + 12 \cdot x + 12 x + 12 \cdot 12 + 30$

Step 2.1.3.1.3

Multiply $12$ by $12$ .

$y = x^{2} + 12 x + 12 x + 144 + 30$

Step 2.1.3.2

Add $12 x$ and $12 x$ .

$y = x^{2} + 24 x + 144 + 30$

Step 2.2

Add $144$ and $30$ .

$y = x^{2} + 24 x + 174$