Algebra Examples

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

Step 1

Expand

$(3 x + 2) (3 x - 2)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

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

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Step 2.1.1

Reorder the factors in the terms

$3 x \cdot - 2$ and

$2 (3 x)$ .

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

Step 2.1.2

Add

$- 2 \cdot 3 x$ and

$2 \cdot 3 x$ .

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

Step 2.1.3

Add

$3 x (3 x)$ and

$0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

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

Step 2.2.2

Multiply

$x$ by

$x$ by adding the exponents.

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Step 2.2.2.1

Move

$x$ .

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

Step 2.2.2.2

Multiply

$x$ by

$x$ .

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

Step 2.2.3

Multiply

$3$ by

$3$ .

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

Step 2.2.4

Multiply

$2$ by

$- 2$ .

$9 x^{2} - 4$