Simplify (a+b)(c-d)

$(a + b) (c - d)$

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

Apply the distributive property.

$a (c - d) + b (c - d)$

Apply the distributive property.

$a c + a (- d) + b (c - d)$

Apply the distributive property.

$a c + a (- d) + b c + b (- d)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$a c - a d + b c + b (- d)$

Rewrite using the commutative property of multiplication.

$a c - a d + b c - b d$