Simplify (xy-z)(xy+z)

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify terms.

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

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

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

Subtract $x y z$ from $x y z$ .

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

Add $x y (x y)$ and $0$ .

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

Simplify each term.

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

Move $x$ .

$x \cdot x y \cdot y - z \cdot z$

Multiply $x$ by $x$ .

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

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

Move $y$ .

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

Multiply $y$ by $y$ .

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

Multiply $z$ by $z$ by adding the exponents.

Move $z$ .

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

Multiply $z$ by $z$ .

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