Precalculus Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

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 $x$ .

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

Step 2.1.2

Move $- 4$ to the left of $x$ .

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

Step 2.1.3

Multiply $- 2$ by $- 4$ .

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

Step 2.2

Subtract $2 x$ from $- 4 x$ .

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

Step 3

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

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

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 $1$ .

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

Step 4.1.1.1.2

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

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

Step 4.1.1.2

Add $2$ and $1$ .

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

Step 4.1.2

Move $- 1$ to the left of $x^{2}$ .

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

Step 4.1.3

Rewrite $- 1 x^{2}$ as $- x^{2}$ .

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

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 $8 x$ .

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