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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $3 x (3 x) + 3 x (- 2 y) + 2 y (3 x) + 2 y (- 2 y)$ .

Reorder the factors in the terms $3 x (- 2 y)$ and $2 y (3 x)$ .

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

Add $- 2 \cdot 3 x y$ and $2 \cdot 3 x y$ .

$3 x (3 x) + 0 + 2 y (- 2 y)$

Add $3 x (3 x)$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$9 x^{2} + 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 2 \cdot - 2 y \cdot y$

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

Move $y$ .

$9 x^{2} + 2 \cdot - 2 (y \cdot y)$

Multiply $y$ by $y$ .

$9 x^{2} + 2 \cdot - 2 y^{2}$

Multiply $2$ by $- 2$ .

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