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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

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

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

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

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

$x \cdot x + 0 + 3 y (- 3 y)$

Add $x \cdot x$ and $0$ .

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

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $3$ by $- 3$ .

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