Find the Product (2x+y)(2x-y)

$(2 x + y) (2 x - y)$

Step 1

Expand $(2 x + y) (2 x - y)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - y) + y (2 x - y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- y) + y (2 x - y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- y) + y (2 x) + y (- y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (- y) + y (2 x) + y (- y)$

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (- y) + y (2 x) + y (- y)$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x (- y) + y (2 x) + y (- y)$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x (- y) + y (2 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot - 1 x y + y (2 x) + y (- y)$

Multiply $2$ by $- 1$ .

$4 x^{2} - 2 x y + y (2 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 2 x y + 2 y x + y (- y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 2 x y + 2 y x - y \cdot y$

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$4 x^{2} - 2 x y + 2 y x - (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} - 2 x y + 2 y x - y^{2}$

Add $- 2 x y$ and $2 y x$ .

Move $y$ .

$4 x^{2} - 2 x y + 2 x y - y^{2}$

Add $- 2 x y$ and $2 x y$ .

$4 x^{2} + 0 - y^{2}$

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

$4 x^{2} - y^{2}$