Finite Math Examples

$- \frac{4 (x + 2) \cdot 1}{2} \cdot (2 x - 6)$

Step 1

Simplify terms.

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Step 1.1

Multiply $4$ by $1$ .

$- \frac{4 (x + 2)}{2} \cdot (2 x - 6)$

Step 1.2

Cancel the common factor of $4$ and $2$ .

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Step 1.2.1

Factor $2$ out of $4 (x + 2)$ .

$- \frac{2 (2 (x + 2))}{2} \cdot (2 x - 6)$

Step 1.2.2

Cancel the common factors.

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Step 1.2.2.1

Factor $2$ out of $2$ .

$- \frac{2 (2 (x + 2))}{2 (1)} \cdot (2 x - 6)$

Step 1.2.2.2

Cancel the common factor.

$- \frac{2 (2 (x + 2))}{2 \cdot 1} \cdot (2 x - 6)$

Step 1.2.2.3

Rewrite the expression.

$- \frac{2 (x + 2)}{1} \cdot (2 x - 6)$

Step 1.2.2.4

Divide $2 (x + 2)$ by $1$ .

$- (2 (x + 2)) \cdot (2 x - 6)$

Step 1.3

Apply the distributive property.

$- (2 x + 2 \cdot 2) \cdot (2 x - 6)$

Step 1.4

Multiply $2$ by $2$ .

$- (2 x + 4) \cdot (2 x - 6)$

Step 1.5

Apply the distributive property.

$(- (2 x) - 1 \cdot 4) \cdot (2 x - 6)$

Step 1.6

Multiply.

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Step 1.6.1

Multiply $2$ by $- 1$ .

$(- 2 x - 1 \cdot 4) \cdot (2 x - 6)$

Step 1.6.2

Multiply $- 1$ by $4$ .

$(- 2 x - 4) \cdot (2 x - 6)$

Step 2

Expand $(- 2 x - 4) (2 x - 6)$ using the FOIL Method.

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Step 2.1

Apply the distributive property.

$- 2 x (2 x - 6) - 4 (2 x - 6)$

Step 2.2

Apply the distributive property.

$- 2 x (2 x) - 2 x \cdot - 6 - 4 (2 x - 6)$

Step 2.3

Apply the distributive property.

$- 2 x (2 x) - 2 x \cdot - 6 - 4 (2 x) - 4 \cdot - 6$

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

Rewrite using the commutative property of multiplication.

$- 2 \cdot 2 x \cdot x - 2 x \cdot - 6 - 4 (2 x) - 4 \cdot - 6$

Step 3.1.2

Multiply $x$ by $x$ by adding the exponents.

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Step 3.1.2.1

Move $x$ .

$- 2 \cdot 2 (x \cdot x) - 2 x \cdot - 6 - 4 (2 x) - 4 \cdot - 6$

Step 3.1.2.2

Multiply $x$ by $x$ .

$- 2 \cdot 2 x^{2} - 2 x \cdot - 6 - 4 (2 x) - 4 \cdot - 6$

Step 3.1.3

Multiply $- 2$ by $2$ .

$- 4 x^{2} - 2 x \cdot - 6 - 4 (2 x) - 4 \cdot - 6$

Step 3.1.4

Multiply $- 6$ by $- 2$ .

$- 4 x^{2} + 12 x - 4 (2 x) - 4 \cdot - 6$

Step 3.1.5

Multiply $2$ by $- 4$ .

$- 4 x^{2} + 12 x - 8 x - 4 \cdot - 6$

Step 3.1.6

Multiply $- 4$ by $- 6$ .

$- 4 x^{2} + 12 x - 8 x + 24$

Step 3.2

Subtract $8 x$ from $12 x$ .

$- 4 x^{2} + 4 x + 24$