Simplify (3x-4y)(3x+4y)

$(3 x - 4 y) (3 x + 4 y)$

Step 1

Expand $(3 x - 4 y) (3 x + 4 y)$ using the FOIL Method.

Apply the distributive property.

$3 x (3 x + 4 y) - 4 y (3 x + 4 y)$

Apply the distributive property.

$3 x (3 x) + 3 x (4 y) - 4 y (3 x + 4 y)$

Apply the distributive property.

$3 x (3 x) + 3 x (4 y) - 4 y (3 x) - 4 y (4 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 \cdot 3 x \cdot x + 3 x (4 y) - 4 y (3 x) - 4 y (4 y)$

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

Move $x$ .

$3 \cdot 3 (x \cdot x) + 3 x (4 y) - 4 y (3 x) - 4 y (4 y)$

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

$9 x^{2} + 3 x (4 y) - 4 y (3 x) - 4 y (4 y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot 4 x y - 4 y (3 x) - 4 y (4 y)$

Multiply $3$ by $4$ .

$9 x^{2} + 12 x y - 4 y (3 x) - 4 y (4 y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 12 x y - 4 \cdot 3 y x - 4 y (4 y)$

Multiply $- 4$ by $3$ .

$9 x^{2} + 12 x y - 12 y x - 4 y (4 y)$

Rewrite using the commutative property of multiplication.

$9 x^{2} + 12 x y - 12 y x - 4 \cdot 4 y \cdot y$

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

Move $y$ .

$9 x^{2} + 12 x y - 12 y x - 4 \cdot 4 (y \cdot y)$

Multiply $y$ by $y$ .

$9 x^{2} + 12 x y - 12 y x - 4 \cdot 4 y^{2}$

Multiply $- 4$ by $4$ .

$9 x^{2} + 12 x y - 12 y x - 16 y^{2}$

Subtract $12 y x$ from $12 x y$ .

Move $y$ .

$9 x^{2} + 12 x y - 12 x y - 16 y^{2}$

Subtract $12 x y$ from $12 x y$ .

$9 x^{2} + 0 - 16 y^{2}$

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

$9 x^{2} - 16 y^{2}$