Precalculus Examples

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

Step 1

Expand $(3 x - 7) (4 - x)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Multiply $4$ by $3$ .

$12 x + 3 x (- x) - 7 \cdot 4 - 7 (- x)$

Step 2.1.2

Rewrite using the commutative property of multiplication.

$12 x + 3 \cdot - 1 x \cdot x - 7 \cdot 4 - 7 (- x)$

Step 2.1.3

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

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Step 2.1.3.1

Move $x$ .

$12 x + 3 \cdot - 1 (x \cdot x) - 7 \cdot 4 - 7 (- x)$

Step 2.1.3.2

Multiply $x$ by $x$ .

$12 x + 3 \cdot - 1 x^{2} - 7 \cdot 4 - 7 (- x)$

Step 2.1.4

Multiply $3$ by $- 1$ .

$12 x - 3 x^{2} - 7 \cdot 4 - 7 (- x)$

Step 2.1.5

Multiply $- 7$ by $4$ .

$12 x - 3 x^{2} - 28 - 7 (- x)$

Step 2.1.6

Multiply $- 1$ by $- 7$ .

$12 x - 3 x^{2} - 28 + 7 x$

Step 2.2

Add $12 x$ and $7 x$ .

$19 x - 3 x^{2} - 28$

Step 3

Reorder $19 x$ and $- 3 x^{2}$ .

$- 3 x^{2} + 19 x - 28$