Basic Math Examples

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

Step 1

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

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Step 1.1

Apply the distributive property.

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

Step 1.2

Apply the distributive property.

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

Step 1.3

Apply the distributive property.

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

Step 2

Combine the opposite terms in $a \cdot a + a (2 b) - 2 b a - 2 b (2 b)$ .

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Step 2.1

Reorder the factors in the terms $a (2 b)$ and $- 2 b a$ .

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

Step 2.2

Subtract $2 a b$ from $2 a b$ .

$a \cdot a + 0 - 2 b (2 b) + 3 b^{2}$

Step 2.3

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

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

Step 3

Simplify each term.

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Step 3.1

Multiply $a$ by $a$ .

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

Step 3.2

Rewrite using the commutative property of multiplication.

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

Step 3.3

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

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Step 3.3.1

Move $b$ .

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

Step 3.3.2

Multiply $b$ by $b$ .

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

Step 3.4

Multiply $- 2$ by $2$ .

$a^{2} - 4 b^{2} + 3 b^{2}$

Step 4

Add $- 4 b^{2}$ and $3 b^{2}$ .

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

Step 5

Since both terms are perfect squares, factor using the difference of squares formula, $a^{2} - b^{2} = (a + b) (a - b)$ where $a = a$ and $b = b$ .

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