Pre-Algebra Examples

(3 a + 2 b) (3 a - 2 b)

$(3 a + 2 b) (3 a - 2 b)$

Step 1

Expand

(3 a + 2 b) (3 a - 2 b)

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

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Step 1.1

Apply the distributive property.

3 a (3 a - 2 b) + 2 b (3 a - 2 b)

$3 a (3 a - 2 b) + 2 b (3 a - 2 b)$

Step 1.2

Apply the distributive property.

3 a (3 a) + 3 a (- 2 b) + 2 b (3 a - 2 b)

$3 a (3 a) + 3 a (- 2 b) + 2 b (3 a - 2 b)$

Step 1.3

Apply the distributive property.

3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)

$3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)$

3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)

$3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)$

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in

3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)

$3 a (3 a) + 3 a (- 2 b) + 2 b (3 a) + 2 b (- 2 b)$ .

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Step 2.1.1

Reorder the factors in the terms

3 a (- 2 b)

$3 a (- 2 b)$ and

2 b (3 a)

$2 b (3 a)$ .

3 a (3 a) - 2 \cdot 3 a b + 2 \cdot 3 a b + 2 b (- 2 b)

$3 a (3 a) - 2 \cdot 3 a b + 2 \cdot 3 a b + 2 b (- 2 b)$

Step 2.1.2

Add

- 2 \cdot 3 a b

$- 2 \cdot 3 a b$ and

2 \cdot 3 a b

$2 \cdot 3 a b$ .

3 a (3 a) + 0 + 2 b (- 2 b)

$3 a (3 a) + 0 + 2 b (- 2 b)$

Step 2.1.3

Add

3 a (3 a)

$3 a (3 a)$ and

0

$0$ .

3 a (3 a) + 2 b (- 2 b)

$3 a (3 a) + 2 b (- 2 b)$

3 a (3 a) + 2 b (- 2 b)

$3 a (3 a) + 2 b (- 2 b)$

Step 2.2

Simplify each term.

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Step 2.2.1

Rewrite using the commutative property of multiplication.

3 \cdot 3 a \cdot a + 2 b (- 2 b)

$3 \cdot 3 a \cdot a + 2 b (- 2 b)$

Step 2.2.2

Multiply

a

$a$ by

a

$a$ by adding the exponents.

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Step 2.2.2.1

Move

a

$a$ .

3 \cdot 3 (a \cdot a) + 2 b (- 2 b)

$3 \cdot 3 (a \cdot a) + 2 b (- 2 b)$

Step 2.2.2.2

Multiply

a

$a$ by

a

$a$ .

3 \cdot 3 a^{2} + 2 b (- 2 b)

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

3 \cdot 3 a^{2} + 2 b (- 2 b)

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

Step 2.2.3

Multiply

3

$3$ by

3

$3$ .

9 a^{2} + 2 b (- 2 b)

$9 a^{2} + 2 b (- 2 b)$

Step 2.2.4

Rewrite using the commutative property of multiplication.

9 a^{2} + 2 \cdot - 2 b \cdot b

$9 a^{2} + 2 \cdot - 2 b \cdot b$

Step 2.2.5

Multiply

b

$b$ by

b

$b$ by adding the exponents.

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Step 2.2.5.1

Move

b

$b$ .

9 a^{2} + 2 \cdot - 2 (b \cdot b)

$9 a^{2} + 2 \cdot - 2 (b \cdot b)$

Step 2.2.5.2

Multiply

b

$b$ by

b

$b$ .

9 a^{2} + 2 \cdot - 2 b^{2}

$9 a^{2} + 2 \cdot - 2 b^{2}$

9 a^{2} + 2 \cdot - 2 b^{2}

$9 a^{2} + 2 \cdot - 2 b^{2}$

Step 2.2.6

Multiply

2

$2$ by

- 2

$- 2$ .

9 a^{2} - 4 b^{2}

$9 a^{2} - 4 b^{2}$

9 a^{2} - 4 b^{2}

$9 a^{2} - 4 b^{2}$

9 a^{2} - 4 b^{2}

$9 a^{2} - 4 b^{2}$