Simplify (8x+y)(8x-y)

$(8 x + y) (8 x - y)$

Step 1

Expand $(8 x + y) (8 x - y)$ using the FOIL Method.

Apply the distributive property.

$8 x (8 x - y) + y (8 x - y)$

Apply the distributive property.

$8 x (8 x) + 8 x (- y) + y (8 x - y)$

Apply the distributive property.

$8 x (8 x) + 8 x (- y) + y (8 x) + y (- y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$8 \cdot 8 x \cdot x + 8 x (- y) + y (8 x) + y (- y)$

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

Move $x$ .

$8 \cdot 8 (x \cdot x) + 8 x (- y) + y (8 x) + y (- y)$

Multiply $x$ by $x$ .

$8 \cdot 8 x^{2} + 8 x (- y) + y (8 x) + y (- y)$

Multiply $8$ by $8$ .

$64 x^{2} + 8 x (- y) + y (8 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$64 x^{2} + 8 \cdot - 1 x y + y (8 x) + y (- y)$

Multiply $8$ by $- 1$ .

$64 x^{2} - 8 x y + y (8 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$64 x^{2} - 8 x y + 8 y x + y (- y)$

Rewrite using the commutative property of multiplication.

$64 x^{2} - 8 x y + 8 y x - y \cdot y$

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

Move $y$ .

$64 x^{2} - 8 x y + 8 y x - (y \cdot y)$

Multiply $y$ by $y$ .

$64 x^{2} - 8 x y + 8 y x - y^{2}$

Add $- 8 x y$ and $8 y x$ .

Move $y$ .

$64 x^{2} - 8 x y + 8 x y - y^{2}$

Add $- 8 x y$ and $8 x y$ .

$64 x^{2} + 0 - y^{2}$

Add $64 x^{2}$ and $0$ .

$64 x^{2} - y^{2}$