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Algebra Examples

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

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

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

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

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Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

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

Simplify and combine like terms.

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Simplify each term.

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Multiply $x$ by $x$ .

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

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

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

Multiply $2$ by $2$ .

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

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

Add $2 x$ and $2 x$ .

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

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

Apply the distributive property.

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

Simplify.

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Multiply $4$ by $- 1$ .

$y = - x^{2} - 4 x - 1 \cdot 4$

Multiply $- 1$ by $4$ .

$y = - x^{2} - 4 x - 4$

$y = - x^{2} - 4 x - 4$

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