Simplify (a-b)(a+b)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

$a \cdot a + a b - b a - b \cdot b$

Step 2

Simplify terms.

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

Reorder the factors in the terms $a b$ and $- b a$ .

$a \cdot a + a b - a b - b \cdot b$

Subtract $a b$ from $a b$ .

$a \cdot a + 0 - b \cdot b$

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

$a \cdot a - b \cdot b$

Simplify each term.

Multiply $a$ by $a$ .

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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