Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $x \cdot x + x \cdot - 4 + 4 x + 4 \cdot - 4$ .

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Step 2.1.1

Reorder the factors in the terms $x \cdot - 4$ and $4 x$ .

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

Step 2.1.2

Add $- 4 x$ and $4 x$ .

$(x \cdot x + 0 + 4 \cdot - 4) (x - 7)$

Step 2.1.3

Add $x \cdot x$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $x$ by $x$ .

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

Step 2.2.2

Multiply $4$ by $- 4$ .

$(x^{2} - 16) (x - 7)$

Step 3

Expand $(x^{2} - 16) (x - 7)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

$x^{2} (x - 7) - 16 (x - 7)$

Step 3.2

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 7 - 16 (x - 7)$

Step 3.3

Apply the distributive property.

$x^{2} x + x^{2} \cdot - 7 - 16 x - 16 \cdot - 7$

Step 4

Simplify each term.

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Step 4.1

Multiply $x^{2}$ by $x$ by adding the exponents.

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Step 4.1.1

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

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Step 4.1.1.1

Raise $x$ to the power of $1$ .

$x^{2} x^{1} + x^{2} \cdot - 7 - 16 x - 16 \cdot - 7$

Step 4.1.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{2 + 1} + x^{2} \cdot - 7 - 16 x - 16 \cdot - 7$

Step 4.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 7 - 16 x - 16 \cdot - 7$

Step 4.2

Move $- 7$ to the left of $x^{2}$ .

$x^{3} - 7 \cdot x^{2} - 16 x - 16 \cdot - 7$

Step 4.3

Multiply $- 16$ by $- 7$ .

$x^{3} - 7 x^{2} - 16 x + 112$