Finite Math Examples

$f (x) = - 4 {(x + 1)}^{2} - 5$

Step 1

Rewrite ${(x + 1)}^{2}$ as $(x + 1) (x + 1)$ .

$f (x) = - 4 ((x + 1) (x + 1)) - 5$

Step 2

Expand $(x + 1) (x + 1)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$f (x) = - 4 (x (x + 1) + 1 (x + 1)) - 5$

Step 2.2

Apply the distributive property.

$f (x) = - 4 (x \cdot x + x \cdot 1 + 1 (x + 1)) - 5$

Step 2.3

Apply the distributive property.

$f (x) = - 4 (x \cdot x + x \cdot 1 + 1 x + 1 \cdot 1) - 5$

Step 3

Simplify and combine like terms.

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Step 3.1

Simplify each term.

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Step 3.1.1

Multiply $x$ by $x$ .

$f (x) = - 4 (x^{2} + x \cdot 1 + 1 x + 1 \cdot 1) - 5$

Step 3.1.2

Multiply $x$ by $1$ .

$f (x) = - 4 (x^{2} + x + 1 x + 1 \cdot 1) - 5$

Step 3.1.3

Multiply $x$ by $1$ .

$f (x) = - 4 (x^{2} + x + x + 1 \cdot 1) - 5$

Step 3.1.4

Multiply $1$ by $1$ .

$f (x) = - 4 (x^{2} + x + x + 1) - 5$

Step 3.2

Add $x$ and $x$ .

$f (x) = - 4 (x^{2} + 2 x + 1) - 5$

Step 4

Apply the distributive property.

$f (x) = - 4 x^{2} - 4 (2 x) - 4 \cdot 1 - 5$

Step 5

Simplify.

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Step 5.1

Multiply $2$ by $- 4$ .

$f (x) = - 4 x^{2} - 8 x - 4 \cdot 1 - 5$

Step 5.2

Multiply $- 4$ by $1$ .

$f (x) = - 4 x^{2} - 8 x - 4 - 5$

Step 6

Subtract $5$ from $- 4$ .

$f (x) = - 4 x^{2} - 8 x - 9$