Simplify (4x+2y)(4x-2y)

$(4 x + 2 y) (4 x - 2 y)$

Step 1

Expand $(4 x + 2 y) (4 x - 2 y)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 2 y) + 2 y (4 x - 2 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 2 y) + 2 y (4 x - 2 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 2 y) + 2 y (4 x) + 2 y (- 2 y)$

Step 2

Simplify terms.

Combine the opposite terms in $4 x (4 x) + 4 x (- 2 y) + 2 y (4 x) + 2 y (- 2 y)$ .

Reorder the factors in the terms $4 x (- 2 y)$ and $2 y (4 x)$ .

$4 x (4 x) - 2 \cdot 4 x y + 2 \cdot 4 x y + 2 y (- 2 y)$

Add $- 2 \cdot 4 x y$ and $2 \cdot 4 x y$ .

$4 x (4 x) + 0 + 2 y (- 2 y)$

Add $4 x (4 x)$ and $0$ .

$4 x (4 x) + 2 y (- 2 y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 2 y (- 2 y)$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 2 y (- 2 y)$

Multiply $x$ by $x$ .

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

Multiply $4$ by $4$ .

$16 x^{2} + 2 y (- 2 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} + 2 \cdot - 2 y \cdot y$

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

Move $y$ .

$16 x^{2} + 2 \cdot - 2 (y \cdot y)$

Multiply $y$ by $y$ .

$16 x^{2} + 2 \cdot - 2 y^{2}$

Multiply $2$ by $- 2$ .

$16 x^{2} - 4 y^{2}$