Simplify (4x+5y)(4x-5y)

$(4 x + 5 y) (4 x - 5 y)$

Step 1

Expand $(4 x + 5 y) (4 x - 5 y)$ using the FOIL Method.

Apply the distributive property.

$4 x (4 x - 5 y) + 5 y (4 x - 5 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 5 y) + 5 y (4 x - 5 y)$

Apply the distributive property.

$4 x (4 x) + 4 x (- 5 y) + 5 y (4 x) + 5 y (- 5 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 \cdot 4 x \cdot x + 4 x (- 5 y) + 5 y (4 x) + 5 y (- 5 y)$

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

Move $x$ .

$4 \cdot 4 (x \cdot x) + 4 x (- 5 y) + 5 y (4 x) + 5 y (- 5 y)$

Multiply $x$ by $x$ .

$4 \cdot 4 x^{2} + 4 x (- 5 y) + 5 y (4 x) + 5 y (- 5 y)$

Multiply $4$ by $4$ .

$16 x^{2} + 4 x (- 5 y) + 5 y (4 x) + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} + 4 \cdot - 5 x y + 5 y (4 x) + 5 y (- 5 y)$

Multiply $4$ by $- 5$ .

$16 x^{2} - 20 x y + 5 y (4 x) + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 20 x y + 5 \cdot 4 y x + 5 y (- 5 y)$

Multiply $5$ by $4$ .

$16 x^{2} - 20 x y + 20 y x + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$16 x^{2} - 20 x y + 20 y x + 5 \cdot - 5 y \cdot y$

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

Move $y$ .

$16 x^{2} - 20 x y + 20 y x + 5 \cdot - 5 (y \cdot y)$

Multiply $y$ by $y$ .

$16 x^{2} - 20 x y + 20 y x + 5 \cdot - 5 y^{2}$

Multiply $5$ by $- 5$ .

$16 x^{2} - 20 x y + 20 y x - 25 y^{2}$

Add $- 20 x y$ and $20 y x$ .

Move $y$ .

$16 x^{2} - 20 x y + 20 x y - 25 y^{2}$

Add $- 20 x y$ and $20 x y$ .

$16 x^{2} + 0 - 25 y^{2}$

Add $16 x^{2}$ and $0$ .

$16 x^{2} - 25 y^{2}$