Pre-Algebra Examples

$7 x - (x - 4) (- x - 3)$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$7 x + (- x - - 4) (- x - 3)$

Step 1.2

Multiply $- 1$ by $- 4$ .

$7 x + (- x + 4) (- x - 3)$

Step 1.3

Expand $(- x + 4) (- x - 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$7 x - x (- x - 3) + 4 (- x - 3)$

Step 1.3.2

Apply the distributive property.

$7 x - x (- x) - x \cdot - 3 + 4 (- x - 3)$

Step 1.3.3

Apply the distributive property.

$7 x - x (- x) - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Rewrite using the commutative property of multiplication.

$7 x - 1 \cdot - 1 x \cdot x - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.2

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

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Step 1.4.1.2.1

Move $x$ .

$7 x - 1 \cdot - 1 (x \cdot x) - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.2.2

Multiply $x$ by $x$ .

$7 x - 1 \cdot - 1 x^{2} - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.3

Multiply $- 1$ by $- 1$ .

$7 x + 1 x^{2} - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.4

Multiply $x^{2}$ by $1$ .

$7 x + x^{2} - x \cdot - 3 + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.5

Multiply $- 3$ by $- 1$ .

$7 x + x^{2} + 3 x + 4 (- x) + 4 \cdot - 3$

Step 1.4.1.6

Multiply $- 1$ by $4$ .

$7 x + x^{2} + 3 x - 4 x + 4 \cdot - 3$

Step 1.4.1.7

Multiply $4$ by $- 3$ .

$7 x + x^{2} + 3 x - 4 x - 12$

Step 1.4.2

Subtract $4 x$ from $3 x$ .

$7 x + x^{2} - x - 12$

Step 2

Subtract $x$ from $7 x$ .

$x^{2} + 6 x - 12$