Find the Product (2x+3y)(2x-3y)

$(2 x + 3 y) (2 x - 3 y)$

Expand $(2 x + 3 y) (2 x - 3 y)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 3 y) + 3 y (2 x - 3 y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- 3 y) + 3 y (2 x - 3 y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- 3 y) + 3 y (2 x) + 3 y (- 3 y)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (- 3 y) + 3 y (2 x) + 3 y (- 3 y)$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (- 3 y) + 3 y (2 x) + 3 y (- 3 y)$

Multiply $x$ by $x$ .

$2 \cdot 2 x^{2} + 2 x (- 3 y) + 3 y (2 x) + 3 y (- 3 y)$

Multiply $2$ by $2$ .

$4 x^{2} + 2 x (- 3 y) + 3 y (2 x) + 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} + 2 \cdot - 3 x y + 3 y (2 x) + 3 y (- 3 y)$

Multiply $2$ by $- 3$ .

$4 x^{2} - 6 x y + 3 y (2 x) + 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 6 x y + 3 \cdot 2 y x + 3 y (- 3 y)$

Multiply $3$ by $2$ .

$4 x^{2} - 6 x y + 6 y x + 3 y (- 3 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 6 x y + 6 y x + 3 \cdot - 3 y \cdot y$

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

Move $y$ .

$4 x^{2} - 6 x y + 6 y x + 3 \cdot - 3 (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} - 6 x y + 6 y x + 3 \cdot - 3 y^{2}$

Multiply $3$ by $- 3$ .

$4 x^{2} - 6 x y + 6 y x - 9 y^{2}$

Add $- 6 x y$ and $6 y x$ .

Move $y$ .

$4 x^{2} - 6 x y + 6 x y - 9 y^{2}$

Add $- 6 x y$ and $6 x y$ .

$4 x^{2} + 0 - 9 y^{2}$

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

$4 x^{2} - 9 y^{2}$