Simplify (a-x)(b-y)

$(a - x) (b - y)$

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

Apply the distributive property.

$a (b - y) - x (b - y)$

Apply the distributive property.

$a b + a (- y) - x (b - y)$

Apply the distributive property.

$a b + a (- y) - x b - x (- y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$a b - a y - x b - x (- y)$

Rewrite using the commutative property of multiplication.

$a b - a y - x b - 1 \cdot - 1 x y$

Multiply $- 1$ by $- 1$ .

$a b - a y - x b + 1 x y$

Multiply $x$ by $1$ .

$a b - a y - x b + x y$