Pre-Algebra Examples

$(9 a - b) (9 a + b)$

Step 1

Expand $(9 a - b) (9 a + b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$9 a (9 a + b) - b (9 a + b)$

Step 1.2

Apply the distributive property.

$9 a (9 a) + 9 a b - b (9 a + b)$

Step 1.3

Apply the distributive property.

$9 a (9 a) + 9 a b - b (9 a) - b \cdot b$

Step 2

Simplify and combine like terms.

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Step 2.1

Simplify each term.

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Step 2.1.1

Rewrite using the commutative property of multiplication.

$9 \cdot 9 a \cdot a + 9 a b - b (9 a) - b \cdot b$

Step 2.1.2

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.2.1

Move $a$ .

$9 \cdot 9 (a \cdot a) + 9 a b - b (9 a) - b \cdot b$

Step 2.1.2.2

Multiply $a$ by $a$ .

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

Step 2.1.3

Multiply $9$ by $9$ .

$81 a^{2} + 9 a b - b (9 a) - b \cdot b$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$81 a^{2} + 9 a b - 1 \cdot 9 b a - b \cdot b$

Step 2.1.5

Multiply $- 1$ by $9$ .

$81 a^{2} + 9 a b - 9 b a - b \cdot b$

Step 2.1.6

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

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Step 2.1.6.1

Move $b$ .

$81 a^{2} + 9 a b - 9 b a - (b \cdot b)$

Step 2.1.6.2

Multiply $b$ by $b$ .

$81 a^{2} + 9 a b - 9 b a - b^{2}$

Step 2.2

Subtract $9 b a$ from $9 a b$ .

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Step 2.2.1

Move $b$ .

$81 a^{2} + 9 a b - 9 a b - b^{2}$

Step 2.2.2

Subtract $9 a b$ from $9 a b$ .

$81 a^{2} + 0 - b^{2}$

Step 2.3

Add $81 a^{2}$ and $0$ .

$81 a^{2} - b^{2}$