Simplify (x+4y)(x-4y)

$(x + 4 y) (x - 4 y)$

Step 1

Expand $(x + 4 y) (x - 4 y)$ using the FOIL Method.

Apply the distributive property.

$x (x - 4 y) + 4 y (x - 4 y)$

Apply the distributive property.

$x \cdot x + x (- 4 y) + 4 y (x - 4 y)$

Apply the distributive property.

$x \cdot x + x (- 4 y) + 4 y x + 4 y (- 4 y)$

Step 2

Simplify terms.

Combine the opposite terms in $x \cdot x + x (- 4 y) + 4 y x + 4 y (- 4 y)$ .

Reorder the factors in the terms $x (- 4 y)$ and $4 y x$ .

$x \cdot x - 4 x y + 4 x y + 4 y (- 4 y)$

Add $- 4 x y$ and $4 x y$ .

$x \cdot x + 0 + 4 y (- 4 y)$

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

$x \cdot x + 4 y (- 4 y)$

Simplify each term.

Multiply $x$ by $x$ .

$x^{2} + 4 y (- 4 y)$

Rewrite using the commutative property of multiplication.

$x^{2} + 4 \cdot - 4 y \cdot y$

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

Move $y$ .

$x^{2} + 4 \cdot - 4 (y \cdot y)$

Multiply $y$ by $y$ .

$x^{2} + 4 \cdot - 4 y^{2}$

Multiply $4$ by $- 4$ .

$x^{2} - 16 y^{2}$