Algebra Examples

(x + 2) (x - 2) (x - 3)

$(x + 2) (x - 2) (x - 3)$

Step 1

Expand

(x + 2) (x - 2)

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

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Step 1.1

Apply the distributive property.

(x (x - 2) + 2 (x - 2)) (x - 3)

$(x (x - 2) + 2 (x - 2)) (x - 3)$

Step 1.2

Apply the distributive property.

(x \cdot x + x \cdot - 2 + 2 (x - 2)) (x - 3)

$(x \cdot x + x \cdot - 2 + 2 (x - 2)) (x - 3)$

Step 1.3

Apply the distributive property.

(x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2) (x - 3)

$(x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2) (x - 3)$

(x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2) (x - 3)

$(x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2) (x - 3)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2

$x \cdot x + x \cdot - 2 + 2 x + 2 \cdot - 2$ .

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Step 2.1.1

Reorder the factors in the terms

x \cdot - 2

$x \cdot - 2$ and

2 x

$2 x$ .

(x \cdot x - 2 x + 2 x + 2 \cdot - 2) (x - 3)

$(x \cdot x - 2 x + 2 x + 2 \cdot - 2) (x - 3)$

Step 2.1.2

Add

- 2 x

$- 2 x$ and

2 x

$2 x$ .

(x \cdot x + 0 + 2 \cdot - 2) (x - 3)

$(x \cdot x + 0 + 2 \cdot - 2) (x - 3)$

Step 2.1.3

Add

x \cdot x

$x \cdot x$ and

0

$0$ .

(x \cdot x + 2 \cdot - 2) (x - 3)

$(x \cdot x + 2 \cdot - 2) (x - 3)$

(x \cdot x + 2 \cdot - 2) (x - 3)

$(x \cdot x + 2 \cdot - 2) (x - 3)$

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply

x

$x$ by

x

$x$ .

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

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

Step 2.2.2

Multiply

2

$2$ by

- 2

$- 2$ .

(x^{2} - 4) (x - 3)

$(x^{2} - 4) (x - 3)$

(x^{2} - 4) (x - 3)

$(x^{2} - 4) (x - 3)$

(x^{2} - 4) (x - 3)

$(x^{2} - 4) (x - 3)$

Step 3

Expand

(x^{2} - 4) (x - 3)

$(x^{2} - 4) (x - 3)$ using the FOIL Method.

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Step 3.1

Apply the distributive property.

x^{2} (x - 3) - 4 (x - 3)

$x^{2} (x - 3) - 4 (x - 3)$

Step 3.2

Apply the distributive property.

x^{2} x + x^{2} \cdot - 3 - 4 (x - 3)

$x^{2} x + x^{2} \cdot - 3 - 4 (x - 3)$

Step 3.3

Apply the distributive property.

x^{2} x + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{2} x + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

x^{2} x + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{2} x + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

Step 4

Simplify each term.

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Step 4.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ by adding the exponents.

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Step 4.1.1

Multiply

x^{2}

$x^{2}$ by

x

$x$ .

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Step 4.1.1.1

Raise

x

$x$ to the power of

1

$1$ .

x^{2} x^{1} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{2} x^{1} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

Step 4.1.1.2

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 - 3 - 4 x - 4 \cdot - 3

$x^{2 + 1} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

x^{2 + 1} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{2 + 1} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

Step 4.1.2

Add

2

$2$ and

1

$1$ .

x^{3} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{3} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

x^{3} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3

$x^{3} + x^{2} \cdot - 3 - 4 x - 4 \cdot - 3$

Step 4.2

Move

- 3

$- 3$ to the left of

x^{2}

$x^{2}$ .

x^{3} - 3 \cdot x^{2} - 4 x - 4 \cdot - 3

$x^{3} - 3 \cdot x^{2} - 4 x - 4 \cdot - 3$

Step 4.3

Multiply

- 4

$- 4$ by

- 3

$- 3$ .

x^{3} - 3 x^{2} - 4 x + 12

$x^{3} - 3 x^{2} - 4 x + 12$

x^{3} - 3 x^{2} - 4 x + 12

$x^{3} - 3 x^{2} - 4 x + 12$

(x + 2) (x - 2) (x - 3)

$(x + 2) (x - 2) (x - 3)$

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[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$