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

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

Step 1

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Multiply $5$ by $5$ .

$25 x^{2} + 5 x (- y) + y (5 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} + 5 \cdot - 1 x y + y (5 x) + y (- y)$

Multiply $5$ by $- 1$ .

$25 x^{2} - 5 x y + y (5 x) + y (- y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} - 5 x y + 5 y x + y (- y)$

Rewrite using the commutative property of multiplication.

$25 x^{2} - 5 x y + 5 y x - y \cdot y$

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

Move $y$ .

$25 x^{2} - 5 x y + 5 y x - (y \cdot y)$

Multiply $y$ by $y$ .

$25 x^{2} - 5 x y + 5 y x - y^{2}$

Add $- 5 x y$ and $5 y x$ .

Move $y$ .

$25 x^{2} - 5 x y + 5 x y - y^{2}$

Add $- 5 x y$ and $5 x y$ .

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

Add $25 x^{2}$ and $0$ .

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