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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $3$ by $3$ .

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

Rewrite using the commutative property of multiplication.

$9 x^{2} + 3 \cdot - 1 x y + y (3 x) + y (- y)$

Multiply $3$ by $- 1$ .

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

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

$9 x^{2} - 3 x y + 3 y x - y^{2}$

Add $- 3 x y$ and $3 y x$ .

Move $y$ .

$9 x^{2} - 3 x y + 3 x y - y^{2}$

Add $- 3 x y$ and $3 x y$ .

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

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

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