Simplify (2a-b)(2a+b)

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

Step 1

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.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $- 1$ by $2$ .

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

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

Move $b$ .

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

Multiply $b$ by $b$ .

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

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 $2 a b$ .

$4 a^{2} + 0 - b^{2}$

Add $4 a^{2}$ and $0$ .

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