Evaluate (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.

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

Step 2

Simplify terms.

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

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

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

Add $- a b$ and $a b$ .

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

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

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

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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