Simplify (2x+5y)(2x-5y)

$(2 x + 5 y) (2 x - 5 y)$

Step 1

Expand $(2 x + 5 y) (2 x - 5 y)$ using the FOIL Method.

Apply the distributive property.

$2 x (2 x - 5 y) + 5 y (2 x - 5 y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- 5 y) + 5 y (2 x - 5 y)$

Apply the distributive property.

$2 x (2 x) + 2 x (- 5 y) + 5 y (2 x) + 5 y (- 5 y)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 \cdot 2 x \cdot x + 2 x (- 5 y) + 5 y (2 x) + 5 y (- 5 y)$

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

Move $x$ .

$2 \cdot 2 (x \cdot x) + 2 x (- 5 y) + 5 y (2 x) + 5 y (- 5 y)$

Multiply $x$ by $x$ .

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

Multiply $2$ by $2$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $2$ by $- 5$ .

$4 x^{2} - 10 x y + 5 y (2 x) + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 10 x y + 5 \cdot 2 y x + 5 y (- 5 y)$

Multiply $5$ by $2$ .

$4 x^{2} - 10 x y + 10 y x + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$4 x^{2} - 10 x y + 10 y x + 5 \cdot - 5 y \cdot y$

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

Move $y$ .

$4 x^{2} - 10 x y + 10 y x + 5 \cdot - 5 (y \cdot y)$

Multiply $y$ by $y$ .

$4 x^{2} - 10 x y + 10 y x + 5 \cdot - 5 y^{2}$

Multiply $5$ by $- 5$ .

$4 x^{2} - 10 x y + 10 y x - 25 y^{2}$

Add $- 10 x y$ and $10 y x$ .

Move $y$ .

$4 x^{2} - 10 x y + 10 x y - 25 y^{2}$

Add $- 10 x y$ and $10 x y$ .

$4 x^{2} + 0 - 25 y^{2}$

Add $4 x^{2}$ and $0$ .

$4 x^{2} - 25 y^{2}$