Simplify (x-y)(x+y)

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

Step 1

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.

$x \cdot x + x y - y x - y \cdot y$

Step 2

Simplify terms.

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

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

$x \cdot x + x y - x y - y \cdot y$

Subtract $x y$ from $x y$ .

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

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

$x \cdot x - y \cdot y$

Simplify each term.

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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