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 $- 4 y (5 x)$ .

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

Subtract $4 \cdot 5 x y$ from $4 \cdot 5 x y$ .

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

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 $4$ .

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