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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- 2 y) + 2 y x + 2 y (- 2 y)$ .

Reorder the factors in the terms $x (- 2 y)$ and $2 y x$ .

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

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

$x \cdot x + 0 + 2 y (- 2 y)$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $2$ by $- 2$ .

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