Expand the Trigonometric Expression (x+y)(x-y)

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

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

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

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

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

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

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

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

Simplify each term.

Multiply $x$ by $x$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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