Basic Math Examples

$(3 a - 5 b) (3 a + 5 b)$

Step 1

Expand $(3 a - 5 b) (3 a + 5 b)$ using the FOIL Method.

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Step 1.1

Apply the distributive property.

$3 a (3 a + 5 b) - 5 b (3 a + 5 b)$

Step 1.2

Apply the distributive property.

$3 a (3 a) + 3 a (5 b) - 5 b (3 a + 5 b)$

Step 1.3

Apply the distributive property.

$3 a (3 a) + 3 a (5 b) - 5 b (3 a) - 5 b (5 b)$

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.

$3 \cdot 3 a \cdot a + 3 a (5 b) - 5 b (3 a) - 5 b (5 b)$

Step 2.1.2

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

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Step 2.1.2.1

Move $a$ .

$3 \cdot 3 (a \cdot a) + 3 a (5 b) - 5 b (3 a) - 5 b (5 b)$

Step 2.1.2.2

Multiply $a$ by $a$ .

$3 \cdot 3 a^{2} + 3 a (5 b) - 5 b (3 a) - 5 b (5 b)$

Step 2.1.3

Multiply $3$ by $3$ .

$9 a^{2} + 3 a (5 b) - 5 b (3 a) - 5 b (5 b)$

Step 2.1.4

Rewrite using the commutative property of multiplication.

$9 a^{2} + 3 \cdot 5 a b - 5 b (3 a) - 5 b (5 b)$

Step 2.1.5

Multiply $3$ by $5$ .

$9 a^{2} + 15 a b - 5 b (3 a) - 5 b (5 b)$

Step 2.1.6

Rewrite using the commutative property of multiplication.

$9 a^{2} + 15 a b - 5 \cdot 3 b a - 5 b (5 b)$

Step 2.1.7

Multiply $- 5$ by $3$ .

$9 a^{2} + 15 a b - 15 b a - 5 b (5 b)$

Step 2.1.8

Rewrite using the commutative property of multiplication.

$9 a^{2} + 15 a b - 15 b a - 5 \cdot 5 b \cdot b$

Step 2.1.9

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

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Step 2.1.9.1

Move $b$ .

$9 a^{2} + 15 a b - 15 b a - 5 \cdot 5 (b \cdot b)$

Step 2.1.9.2

Multiply $b$ by $b$ .

$9 a^{2} + 15 a b - 15 b a - 5 \cdot 5 b^{2}$

Step 2.1.10

Multiply $- 5$ by $5$ .

$9 a^{2} + 15 a b - 15 b a - 25 b^{2}$

Step 2.2

Subtract $15 b a$ from $15 a b$ .

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Step 2.2.1

Move $b$ .

$9 a^{2} + 15 a b - 15 a b - 25 b^{2}$

Step 2.2.2

Subtract $15 a b$ from $15 a b$ .

$9 a^{2} + 0 - 25 b^{2}$

Step 2.3

Add $9 a^{2}$ and $0$ .

$9 a^{2} - 25 b^{2}$