Simplify (a-b)^2

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

Step 1

Rewrite ${(a - b)}^{2}$ as $(a - b) (a - b)$ .

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

Step 2

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 3

Simplify and combine like terms.

Simplify each term.

Multiply $a$ by $a$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $b$ .

$a^{2} - a b - b a - 1 \cdot - 1 (b \cdot b)$

Multiply $b$ by $b$ .

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

Multiply $- 1$ by $- 1$ .

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

Multiply $b^{2}$ by $1$ .

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

Subtract $b a$ from $- a b$ .

Move $b$ .

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

Subtract $a b$ from $- a b$ .

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