Algebra Examples

$f (x) = 3 {(x - 2)}^{2} + 4$

Simplify each term.

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

$y = 3 ((x - 2) (x - 2)) + 4$

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

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Apply the distributive property.

$y = 3 (x (x - 2) - 2 (x - 2)) + 4$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot - 2 - 2 (x - 2)) + 4$

Apply the distributive property.

$y = 3 (x \cdot x + x \cdot - 2 - 2 x - 2 \cdot - 2) + 4$

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

$y = 3 (x^{2} + x \cdot - 2 - 2 x - 2 \cdot - 2) + 4$

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

$y = 3 (x^{2} - 2 \cdot x - 2 x - 2 \cdot - 2) + 4$

Multiply $- 2$ by $- 2$ .

$y = 3 (x^{2} - 2 x - 2 x + 4) + 4$

Subtract $2 x$ from $- 2 x$ .

$y = 3 (x^{2} - 4 x + 4) + 4$

Apply the distributive property.

$y = 3 x^{2} + 3 (- 4 x) + 3 \cdot 4 + 4$

Simplify.

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Multiply $- 4$ by $3$ .

$y = 3 x^{2} - 12 x + 3 \cdot 4 + 4$

Multiply $3$ by $4$ .

$y = 3 x^{2} - 12 x + 12 + 4$

Add $12$ and $4$ .

$y = 3 x^{2} - 12 x + 16$

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