Simplify (9x+y)(9x-y)

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $9$ by $9$ .

$81 x^{2} + 9 x (- y) + y (9 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$81 x^{2} + 9 \cdot - 1 x y + y (9 x) + y (- y)$

Multiply $9$ by $- 1$ .

$81 x^{2} - 9 x y + y (9 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$81 x^{2} - 9 x y + 9 y x + y (- y)$

Rewrite using the commutative property of multiplication.

$81 x^{2} - 9 x y + 9 y x - y \cdot y$

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

Move $y$ .

$81 x^{2} - 9 x y + 9 y x - (y \cdot y)$

Multiply $y$ by $y$ .

$81 x^{2} - 9 x y + 9 y x - y^{2}$

Add $- 9 x y$ and $9 y x$ .

Move $y$ .

$81 x^{2} - 9 x y + 9 x y - y^{2}$

Add $- 9 x y$ and $9 x y$ .

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

Add $81 x^{2}$ and $0$ .

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