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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify terms.

Combine the opposite terms in $5 x (5 x) + 5 x (- 4 y) + 4 y (5 x) + 4 y (- 4 y)$ .

Reorder the factors in the terms $5 x (- 4 y)$ and $4 y (5 x)$ .

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

Add $- 4 \cdot 5 x y$ and $4 \cdot 5 x y$ .

$5 x (5 x) + 0 + 4 y (- 4 y)$

Add $5 x (5 x)$ and $0$ .

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

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

$25 x^{2} + 4 y (- 4 y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 4 \cdot - 4 y \cdot y$

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

Move $y$ .

$25 x^{2} + 4 \cdot - 4 (y \cdot y)$

Multiply $y$ by $y$ .

$25 x^{2} + 4 \cdot - 4 y^{2}$

Multiply $4$ by $- 4$ .

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