Pre-Algebra Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Simplify terms.

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Step 2.1

Combine the opposite terms in $a \cdot a + a (3 b) - 3 b a - 3 b (3 b)$ .

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Step 2.1.1

Reorder the factors in the terms $a (3 b)$ and $- 3 b a$ .

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

Step 2.1.2

Subtract $3 a b$ from $3 a b$ .

$a \cdot a + 0 - 3 b (3 b)$

Step 2.1.3

Add $a \cdot a$ and $0$ .

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

Step 2.2

Simplify each term.

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Step 2.2.1

Multiply $a$ by $a$ .

$a^{2} - 3 b (3 b)$

Step 2.2.2

Rewrite using the commutative property of multiplication.

$a^{2} - 3 \cdot 3 b \cdot b$

Step 2.2.3

Multiply $b$ by $b$ by adding the exponents.

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Step 2.2.3.1

Move $b$ .

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

Step 2.2.3.2

Multiply $b$ by $b$ .

$a^{2} - 3 \cdot 3 b^{2}$

Step 2.2.4

Multiply $- 3$ by $3$ .

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