Precalculus Examples

$(x + 6) (x + 1) (x - 2)$

Step 1

Expand $(x + 6) (x + 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(x (x + 1) + 6 (x + 1)) (x - 2)$

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $x$ by $x$ .

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

Step 2.1.2

Multiply $x$ by $1$ .

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

Step 2.1.3

Multiply $6$ by $1$ .

$(x^{2} + x + 6 x + 6) (x - 2)$

Step 2.2

Add $x$ and $6 x$ .

$(x^{2} + 7 x + 6) (x - 2)$

Step 3

Expand $(x^{2} + 7 x + 6) (x - 2)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 2 + 7 x \cdot x + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4

Simplify terms.

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Step 4.1

Simplify each term.

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Step 4.1.1

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

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Step 4.1.1.1

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

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Step 4.1.1.1.1

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

$x^{2} x^{1} + x^{2} \cdot - 2 + 7 x \cdot x + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 2 + 7 x \cdot x + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 2 + 7 x \cdot x + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.2

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

$x^{3} - 2 \cdot x^{2} + 7 x \cdot x + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.3

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

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Step 4.1.3.1

Move $x$ .

$x^{3} - 2 x^{2} + 7 (x \cdot x) + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 2 x^{2} + 7 x^{2} + 7 x \cdot - 2 + 6 x + 6 \cdot - 2$

Step 4.1.4

Multiply $- 2$ by $7$ .

$x^{3} - 2 x^{2} + 7 x^{2} - 14 x + 6 x + 6 \cdot - 2$

Step 4.1.5

Multiply $6$ by $- 2$ .

$x^{3} - 2 x^{2} + 7 x^{2} - 14 x + 6 x - 12$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Add $- 2 x^{2}$ and $7 x^{2}$ .

$x^{3} + 5 x^{2} - 14 x + 6 x - 12$

Step 4.2.2

Add $- 14 x$ and $6 x$ .

$x^{3} + 5 x^{2} - 8 x - 12$