Algebra Examples

$f (x) = {(x + 2)}^{2} - 1$

Step 1

To write a polynomial in standard form, simplify and then arrange the terms in descending order.

$f (x) = a x^{2} + b x + c$

Step 2

Simplify each term.

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Step 2.1

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

$f (x) = (x + 2) (x + 2) - 1$

Step 2.2

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

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Step 2.2.1

Apply the distributive property.

$f (x) = x (x + 2) + 2 (x + 2) - 1$

Step 2.2.2

Apply the distributive property.

$f (x) = x \cdot x + x \cdot 2 + 2 (x + 2) - 1$

Step 2.2.3

Apply the distributive property.

$f (x) = x \cdot x + x \cdot 2 + 2 x + 2 \cdot 2 - 1$

Step 2.3

Simplify and combine like terms.

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Step 2.3.1

Simplify each term.

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Step 2.3.1.1

Multiply $x$ by $x$ .

$f (x) = x^{2} + x \cdot 2 + 2 x + 2 \cdot 2 - 1$

Step 2.3.1.2

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

$f (x) = x^{2} + 2 \cdot x + 2 x + 2 \cdot 2 - 1$

Step 2.3.1.3

Multiply $2$ by $2$ .

$f (x) = x^{2} + 2 x + 2 x + 4 - 1$

Step 2.3.2

Add $2 x$ and $2 x$ .

$f (x) = x^{2} + 4 x + 4 - 1$

Step 3

Subtract $1$ from $4$ .

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