Simplify (4x-3y)(4x+3y)

$(4 x - 3 y) (4 x + 3 y)$

Step 1

Expand $(4 x - 3 y) (4 x + 3 y)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x + 3 y) - 3 y (4 x + 3 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (3 y) - 3 y (4 x + 3 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (3 y) - 3 y (4 x) - 3 y (3 y)$

Step 2

Simplify terms.

Combine the opposite terms in $4 x (4 x) + 4 x (3 y) - 3 y (4 x) - 3 y (3 y)$ .

Reorder the factors in the terms $4 x (3 y)$ and $- 3 y (4 x)$ .

$4 x (4 x) + 3 \cdot 4 x y - 3 \cdot 4 x y - 3 y (3 y)$

Subtract $3 \cdot 4 x y$ from $3 \cdot 4 x y$ .

$4 x (4 x) + 0 - 3 y (3 y)$

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

$4 x (4 x) - 3 y (3 y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x - 3 y (3 y)$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) - 3 y (3 y)$

Multiply $x$ by $x$ .

$4 \cdot 4 x^{2} - 3 y (3 y)$

Multiply $4$ by $4$ .

$16 x^{2} - 3 y (3 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 3 \cdot 3 y \cdot y$

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

Move $y$ .

$16 x^{2} - 3 \cdot 3 (y \cdot y)$

Multiply $y$ by $y$ .

$16 x^{2} - 3 \cdot 3 y^{2}$

Multiply $- 3$ by $3$ .

$16 x^{2} - 9 y^{2}$