Precalculus Examples

(x - 2) (x - 4) (x - 1)

$(x - 2) (x - 4) (x - 1)$

Step 1

Expand

(x - 2) (x - 4)

$(x - 2) (x - 4)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

(x (x - 4) - 2 (x - 4)) (x - 1)

$(x (x - 4) - 2 (x - 4)) (x - 1)$

Step 1.2

Apply the distributive property.

(x \cdot x + x \cdot - 4 - 2 (x - 4)) (x - 1)

$(x \cdot x + x \cdot - 4 - 2 (x - 4)) (x - 1)$

Step 1.3

Apply the distributive property.

(x \cdot x + x \cdot - 4 - 2 x - 2 \cdot - 4) (x - 1)

$(x \cdot x + x \cdot - 4 - 2 x - 2 \cdot - 4) (x - 1)$

(x \cdot x + x \cdot - 4 - 2 x - 2 \cdot - 4) (x - 1)

$(x \cdot x + x \cdot - 4 - 2 x - 2 \cdot - 4) (x - 1)$

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

$x$ by

x

$x$ .

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

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

Step 2.1.2

Move

- 4

$- 4$ to the left of

x

$x$ .

(x^{2} - 4 \cdot x - 2 x - 2 \cdot - 4) (x - 1)

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

Step 2.1.3

Multiply

- 2

$- 2$ by

- 4

$- 4$ .

(x^{2} - 4 x - 2 x + 8) (x - 1)

$(x^{2} - 4 x - 2 x + 8) (x - 1)$

(x^{2} - 4 x - 2 x + 8) (x - 1)

$(x^{2} - 4 x - 2 x + 8) (x - 1)$

Step 2.2

Subtract

2 x

$2 x$ from

- 4 x

$- 4 x$ .

(x^{2} - 6 x + 8) (x - 1)

$(x^{2} - 6 x + 8) (x - 1)$

(x^{2} - 6 x + 8) (x - 1)

$(x^{2} - 6 x + 8) (x - 1)$

Step 3

Expand

(x^{2} - 6 x + 8) (x - 1)

$(x^{2} - 6 x + 8) (x - 1)$ by multiplying each term in the first expression by each term in the second expression.

x^{2} x + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{2} x + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

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}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 4.1.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ .

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Step 4.1.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

x^{2} x^{1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{2} x^{1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.1.1.2

Use the power rule

a^{m} a^{n} = a^{m + n}

$a^{m} a^{n} = a^{m + n}$ to combine exponents.

x^{2 + 1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{2 + 1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

x^{2 + 1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{2 + 1} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.1.2

Add

2

$2$ and

1

$1$ .

x^{3} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{3} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

x^{3} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{3} + x^{2} \cdot - 1 - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.2

Move

- 1

$- 1$ to the left of

x^{2}

$x^{2}$ .

x^{3} - 1 \cdot x^{2} - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{3} - 1 \cdot x^{2} - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.3

Rewrite

- 1 x^{2}

$- 1 x^{2}$ as

- x^{2}

$- x^{2}$ .

x^{3} - x^{2} - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1

$x^{3} - x^{2} - 6 x \cdot x - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.4

Multiply

$x$ by

$x$ by adding the exponents.

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Step 4.1.4.1

Move

$x$ .

$x^{3} - x^{2} - 6 (x \cdot x) - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.4.2

Multiply

$x$ by

$x$ .

$x^{3} - x^{2} - 6 x^{2} - 6 x \cdot - 1 + 8 x + 8 \cdot - 1$

Step 4.1.5

Multiply

$- 1$ by

$- 6$ .

$x^{3} - x^{2} - 6 x^{2} + 6 x + 8 x + 8 \cdot - 1$

Step 4.1.6

Multiply

$8$ by

$- 1$ .

$x^{3} - x^{2} - 6 x^{2} + 6 x + 8 x - 8$

Step 4.2

Simplify by adding terms.

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Step 4.2.1

Subtract

$6 x^{2}$ from

$- x^{2}$ .

$x^{3} - 7 x^{2} + 6 x + 8 x - 8$

Step 4.2.2

Add

$6 x$ and

$8 x$ .

$x^{3} - 7 x^{2} + 14 x - 8$