Algebra Examples

(3 x + 1) (3 x - 1)

$(3 x + 1) (3 x - 1)$

Step 1

Expand

(3 x + 1) (3 x - 1)

$(3 x + 1) (3 x - 1)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

3 x (3 x - 1) + 1 (3 x - 1)

$3 x (3 x - 1) + 1 (3 x - 1)$

Step 1.2

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 1 + 1 (3 x - 1)

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x - 1)$

Step 1.3

Apply the distributive property.

3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1$

3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1

$3 x (3 x) + 3 x \cdot - 1 + 1 (3 x) + 1 \cdot - 1$ .

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Step 2.1.1

Reorder the factors in the terms

3 x \cdot - 1

$3 x \cdot - 1$ and

1 (3 x)

$1 (3 x)$ .

3 x (3 x) - 1 \cdot 3 x + 1 \cdot 3 x + 1 \cdot - 1

$3 x (3 x) - 1 \cdot 3 x + 1 \cdot 3 x + 1 \cdot - 1$

Step 2.1.2

Add

- 1 \cdot 3 x

$- 1 \cdot 3 x$ and

1 \cdot 3 x

$1 \cdot 3 x$ .

3 x (3 x) + 0 + 1 \cdot - 1

$3 x (3 x) + 0 + 1 \cdot - 1$

Step 2.1.3

Add

3 x (3 x)

$3 x (3 x)$ and

0

$0$ .

3 x (3 x) + 1 \cdot - 1

$3 x (3 x) + 1 \cdot - 1$

3 x (3 x) + 1 \cdot - 1

$3 x (3 x) + 1 \cdot - 1$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

3 \cdot 3 x \cdot x + 1 \cdot - 1

$3 \cdot 3 x \cdot x + 1 \cdot - 1$

Step 2.2.2

Multiply

x

$x$ by

x

$x$ by adding the exponents.

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Step 2.2.2.1

Move

x

$x$ .

3 \cdot 3 (x \cdot x) + 1 \cdot - 1

$3 \cdot 3 (x \cdot x) + 1 \cdot - 1$

Step 2.2.2.2

Multiply

x

$x$ by

x

$x$ .

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

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

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

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

Step 2.2.3

Multiply

3

$3$ by

3

$3$ .

9 x^{2} + 1 \cdot - 1

$9 x^{2} + 1 \cdot - 1$

Step 2.2.4

Multiply

- 1

$- 1$ by

1

$1$ .

9 x^{2} - 1

$9 x^{2} - 1$

9 x^{2} - 1

$9 x^{2} - 1$

9 x^{2} - 1

$9 x^{2} - 1$