Simplify (3A+4B)(3A-4B)

$(3 A + 4 B) (3 A - 4 B)$

Step 1

Expand $(3 A + 4 B) (3 A - 4 B)$ using the FOIL Method.

Apply the distributive property.

$3 A (3 A - 4 B) + 4 B (3 A - 4 B)$

Apply the distributive property.

$3 A (3 A) + 3 A (- 4 B) + 4 B (3 A - 4 B)$

Apply the distributive property.

$3 A (3 A) + 3 A (- 4 B) + 4 B (3 A) + 4 B (- 4 B)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 A \cdot A + 3 A (- 4 B) + 4 B (3 A) + 4 B (- 4 B)$

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

Move $A$ .

$3 \cdot 3 (A \cdot A) + 3 A (- 4 B) + 4 B (3 A) + 4 B (- 4 B)$

Multiply $A$ by $A$ .

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

Multiply $3$ by $3$ .

$9 A^{2} + 3 A (- 4 B) + 4 B (3 A) + 4 B (- 4 B)$

Rewrite using the commutative property of multiplication.

$9 A^{2} + 3 \cdot - 4 A B + 4 B (3 A) + 4 B (- 4 B)$

Multiply $3$ by $- 4$ .

$9 A^{2} - 12 A B + 4 B (3 A) + 4 B (- 4 B)$

Rewrite using the commutative property of multiplication.

$9 A^{2} - 12 A B + 4 \cdot 3 B A + 4 B (- 4 B)$

Multiply $4$ by $3$ .

$9 A^{2} - 12 A B + 12 B A + 4 B (- 4 B)$

Rewrite using the commutative property of multiplication.

$9 A^{2} - 12 A B + 12 B A + 4 \cdot - 4 B \cdot B$

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

Move $B$ .

$9 A^{2} - 12 A B + 12 B A + 4 \cdot - 4 (B \cdot B)$

Multiply $B$ by $B$ .

$9 A^{2} - 12 A B + 12 B A + 4 \cdot - 4 B^{2}$

Multiply $4$ by $- 4$ .

$9 A^{2} - 12 A B + 12 B A - 16 B^{2}$

Add $- 12 A B$ and $12 B A$ .

Move $B$ .

$9 A^{2} - 12 A B + 12 A B - 16 B^{2}$

Add $- 12 A B$ and $12 A B$ .

$9 A^{2} + 0 - 16 B^{2}$

Add $9 A^{2}$ and $0$ .

$9 A^{2} - 16 B^{2}$