Simplify (x-a)(x-b)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

$x^{2} - x b - a x - 1 \cdot - 1 a b$

Multiply $- 1$ by $- 1$ .

$x^{2} - x b - a x + 1 a b$

Multiply $a$ by $1$ .

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