Find the Product (2A+3B)(2A-3B)

$(2 A + 3 B) (2 A - 3 B)$

Expand $(2 A + 3 B) (2 A - 3 B)$ using the FOIL Method.

Apply the distributive property.

$2 A (2 A - 3 B) + 3 B (2 A - 3 B)$

Apply the distributive property.

$2 A (2 A) + 2 A (- 3 B) + 3 B (2 A - 3 B)$

Apply the distributive property.

$2 A (2 A) + 2 A (- 3 B) + 3 B (2 A) + 3 B (- 3 B)$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 A \cdot A + 2 A (- 3 B) + 3 B (2 A) + 3 B (- 3 B)$

Multiply $A$ by $A$ by adding the exponents.

Move $A$ .

$2 \cdot 2 (A \cdot A) + 2 A (- 3 B) + 3 B (2 A) + 3 B (- 3 B)$

Multiply $A$ by $A$ .

$2 \cdot 2 A^{2} + 2 A (- 3 B) + 3 B (2 A) + 3 B (- 3 B)$

Multiply $2$ by $2$ .

$4 A^{2} + 2 A (- 3 B) + 3 B (2 A) + 3 B (- 3 B)$

Rewrite using the commutative property of multiplication.

$4 A^{2} + 2 \cdot - 3 A B + 3 B (2 A) + 3 B (- 3 B)$

Multiply $2$ by $- 3$ .

$4 A^{2} - 6 A B + 3 B (2 A) + 3 B (- 3 B)$

Rewrite using the commutative property of multiplication.

$4 A^{2} - 6 A B + 3 \cdot 2 B A + 3 B (- 3 B)$

Multiply $3$ by $2$ .

$4 A^{2} - 6 A B + 6 B A + 3 B (- 3 B)$

Rewrite using the commutative property of multiplication.

$4 A^{2} - 6 A B + 6 B A + 3 \cdot - 3 B \cdot B$

Multiply $B$ by $B$ by adding the exponents.

Move $B$ .

$4 A^{2} - 6 A B + 6 B A + 3 \cdot - 3 (B \cdot B)$

Multiply $B$ by $B$ .

$4 A^{2} - 6 A B + 6 B A + 3 \cdot - 3 B^{2}$

Multiply $3$ by $- 3$ .

$4 A^{2} - 6 A B + 6 B A - 9 B^{2}$

Add $- 6 A B$ and $6 B A$ .

Move $B$ .

$4 A^{2} - 6 A B + 6 A B - 9 B^{2}$

Add $- 6 A B$ and $6 A B$ .

$4 A^{2} + 0 - 9 B^{2}$

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

$4 A^{2} - 9 B^{2}$