Precalculus Examples

$(x - 6) (x + 3) (x - 5)$

Step 1

Expand $(x - 6) (x + 3)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$(x (x + 3) - 6 (x + 3)) (x - 5)$

Step 1.2

Apply the distributive property.

$(x \cdot x + x \cdot 3 - 6 (x + 3)) (x - 5)$

Step 1.3

Apply the distributive property.

$(x \cdot x + x \cdot 3 - 6 x - 6 \cdot 3) (x - 5)$

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 $x$ .

$(x^{2} + x \cdot 3 - 6 x - 6 \cdot 3) (x - 5)$

Step 2.1.2

Move $3$ to the left of $x$ .

$(x^{2} + 3 \cdot x - 6 x - 6 \cdot 3) (x - 5)$

Step 2.1.3

Multiply $- 6$ by $3$ .

$(x^{2} + 3 x - 6 x - 18) (x - 5)$

Step 2.2

Subtract $6 x$ from $3 x$ .

$(x^{2} - 3 x - 18) (x - 5)$

Step 3

Expand $(x^{2} - 3 x - 18) (x - 5)$ by multiplying each term in the first expression by each term in the second expression.

$x^{2} x + x^{2} \cdot - 5 - 3 x \cdot x - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

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 $1$ .

$x^{2} x^{1} + x^{2} \cdot - 5 - 3 x \cdot x - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.1.1.2

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

$x^{2 + 1} + x^{2} \cdot - 5 - 3 x \cdot x - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.1.2

Add $2$ and $1$ .

$x^{3} + x^{2} \cdot - 5 - 3 x \cdot x - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.2

Move $- 5$ to the left of $x^{2}$ .

$x^{3} - 5 \cdot x^{2} - 3 x \cdot x - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.3

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

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Step 4.1.3.1

Move $x$ .

$x^{3} - 5 x^{2} - 3 (x \cdot x) - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.3.2

Multiply $x$ by $x$ .

$x^{3} - 5 x^{2} - 3 x^{2} - 3 x \cdot - 5 - 18 x - 18 \cdot - 5$

Step 4.1.4

Multiply $- 5$ by $- 3$ .

$x^{3} - 5 x^{2} - 3 x^{2} + 15 x - 18 x - 18 \cdot - 5$

Step 4.1.5

Multiply $- 18$ by $- 5$ .

$x^{3} - 5 x^{2} - 3 x^{2} + 15 x - 18 x + 90$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract $3 x^{2}$ from $- 5 x^{2}$ .

$x^{3} - 8 x^{2} + 15 x - 18 x + 90$

Step 4.2.2

Subtract $18 x$ from $15 x$ .

$x^{3} - 8 x^{2} - 3 x + 90$