Evaluate (2a-b)^2

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

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

$(2 a - b) (2 a - b)$

Expand $(2 a - b) (2 a - b)$ using the FOIL Method.

Apply the distributive property.

$2 a (2 a - b) - b (2 a - b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- b) - b (2 a - b)$

Apply the distributive property.

$2 a (2 a) + 2 a (- b) - b (2 a) - b (- b)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 a \cdot a + 2 a (- b) - b (2 a) - b (- b)$

Multiply $a$ by $a$ by adding the exponents.

Move $a$ .

$2 \cdot 2 (a \cdot a) + 2 a (- b) - b (2 a) - b (- b)$

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

$4 a^{2} + 2 a (- b) - b (2 a) - b (- b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} + 2 \cdot - 1 a b - b (2 a) - b (- b)$

Multiply $2$ by $- 1$ .

$4 a^{2} - 2 a b - b (2 a) - b (- b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 2 a b - 1 \cdot 2 b a - b (- b)$

Multiply $- 1$ by $2$ .

$4 a^{2} - 2 a b - 2 b a - b (- b)$

Rewrite using the commutative property of multiplication.

$4 a^{2} - 2 a b - 2 b a - 1 \cdot - 1 b \cdot b$

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

Move $b$ .

$4 a^{2} - 2 a b - 2 b a - 1 \cdot - 1 (b \cdot b)$

Multiply $b$ by $b$ .

$4 a^{2} - 2 a b - 2 b a - 1 \cdot - 1 b^{2}$

Multiply $- 1$ by $- 1$ .

$4 a^{2} - 2 a b - 2 b a + 1 b^{2}$

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

$4 a^{2} - 2 a b - 2 b a + b^{2}$

Subtract $2 b a$ from $- 2 a b$ .

Move $b$ .

$4 a^{2} - 2 a b - 2 a b + b^{2}$

Subtract $2 a b$ from $- 2 a b$ .

$4 a^{2} - 4 a b + b^{2}$