Algebra Examples

$f (x) = 3 {(x + 3)}^{2} - 2$

Step 1

Rewrite the function as an equation.

$y = 3 {(x + 3)}^{2} - 2$

Step 2

Simplify $3 {(x + 3)}^{2} - 2$ .

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite ${(x + 3)}^{2}$ as $(x + 3) (x + 3)$ .

$y = 3 ((x + 3) (x + 3)) - 2$

Step 2.1.2

Expand $(x + 3) (x + 3)$ using the FOIL Method.

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Step 2.1.2.1

Apply the distributive property.

$y = 3 (x (x + 3) + 3 (x + 3)) - 2$

Step 2.1.2.2

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 3 + 3 (x + 3)) - 2$

Step 2.1.2.3

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 2$

$y = 3 (x \cdot x + x \cdot 3 + 3 x + 3 \cdot 3) - 2$

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 $x$ .

$y = 3 (x^{2} + x \cdot 3 + 3 x + 3 \cdot 3) - 2$

Step 2.1.3.1.2

Move $3$ to the left of $x$ .

$y = 3 (x^{2} + 3 \cdot x + 3 x + 3 \cdot 3) - 2$

Step 2.1.3.1.3

Multiply $3$ by $3$ .

$y = 3 (x^{2} + 3 x + 3 x + 9) - 2$

$y = 3 (x^{2} + 3 x + 3 x + 9) - 2$

Step 2.1.3.2

Add $3 x$ and $3 x$ .

$y = 3 (x^{2} + 6 x + 9) - 2$

$y = 3 (x^{2} + 6 x + 9) - 2$

Step 2.1.4

Apply the distributive property.

$y = 3 x^{2} + 3 (6 x) + 3 \cdot 9 - 2$

Step 2.1.5

Simplify.

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Step 2.1.5.1

Multiply $6$ by $3$ .

$y = 3 x^{2} + 18 x + 3 \cdot 9 - 2$

Step 2.1.5.2

Multiply $3$ by $9$ .

$y = 3 x^{2} + 18 x + 27 - 2$

$y = 3 x^{2} + 18 x + 27 - 2$

$y = 3 x^{2} + 18 x + 27 - 2$

Step 2.2

Subtract $2$ from $27$ .

$y = 3 x^{2} + 18 x + 25$

$y = 3 x^{2} + 18 x + 25$

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