Find the Product (6xy-9z)(6xy+9z)

$(6 x y - 9 z) (6 x y + 9 z)$

Step 1

Expand $(6 x y - 9 z) (6 x y + 9 z)$ using the FOIL Method.

Apply the distributive property.

$6 x y (6 x y + 9 z) - 9 z (6 x y + 9 z)$

Apply the distributive property.

$6 x y (6 x y) + 6 x y (9 z) - 9 z (6 x y + 9 z)$

Apply the distributive property.

$6 x y (6 x y) + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $x$ .

$6 (x \cdot x) y (6 y) + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

Multiply $x$ by $x$ .

$6 x^{2} y (6 y) + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

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

Move $y$ .

$6 x^{2} (y \cdot y) \cdot 6 + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

Multiply $y$ by $y$ .

$6 x^{2} y^{2} \cdot 6 + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

Multiply $6$ by $6$ .

$36 x^{2} y^{2} + 6 x y (9 z) - 9 z (6 x y) - 9 z (9 z)$

Multiply $9$ by $6$ .

$36 x^{2} y^{2} + 54 x y z - 9 z (6 x y) - 9 z (9 z)$

Multiply $6$ by $- 9$ .

$36 x^{2} y^{2} + 54 x y z - 54 z (x y) - 9 z (9 z)$

Rewrite using the commutative property of multiplication.

$36 x^{2} y^{2} + 54 x y z - 54 z x y - 9 \cdot 9 z \cdot z$

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

Move $z$ .

$36 x^{2} y^{2} + 54 x y z - 54 z x y - 9 \cdot 9 (z \cdot z)$

Multiply $z$ by $z$ .

$36 x^{2} y^{2} + 54 x y z - 54 z x y - 9 \cdot 9 z^{2}$

Multiply $- 9$ by $9$ .

$36 x^{2} y^{2} + 54 x y z - 54 z x y - 81 z^{2}$

Subtract $54 z x y$ from $54 x y z$ .

Move $z$ .

$36 x^{2} y^{2} + 54 x y z - 54 x y z - 81 z^{2}$

Subtract $54 x y z$ from $54 x y z$ .

$36 x^{2} y^{2} + 0 - 81 z^{2}$

Add $36 x^{2} y^{2}$ and $0$ .

$36 x^{2} y^{2} - 81 z^{2}$