Simplify (7x+5y)(7x-5y)

$(7 x + 5 y) (7 x - 5 y)$

Step 1

Expand $(7 x + 5 y) (7 x - 5 y)$ using the FOIL Method.

Apply the distributive property.

$7 x (7 x - 5 y) + 5 y (7 x - 5 y)$

Apply the distributive property.

$7 x (7 x) + 7 x (- 5 y) + 5 y (7 x - 5 y)$

Apply the distributive property.

$7 x (7 x) + 7 x (- 5 y) + 5 y (7 x) + 5 y (- 5 y)$

Step 2

Simplify terms.

Combine the opposite terms in $7 x (7 x) + 7 x (- 5 y) + 5 y (7 x) + 5 y (- 5 y)$ .

Reorder the factors in the terms $7 x (- 5 y)$ and $5 y (7 x)$ .

$7 x (7 x) - 5 \cdot 7 x y + 5 \cdot 7 x y + 5 y (- 5 y)$

Add $- 5 \cdot 7 x y$ and $5 \cdot 7 x y$ .

$7 x (7 x) + 0 + 5 y (- 5 y)$

Add $7 x (7 x)$ and $0$ .

$7 x (7 x) + 5 y (- 5 y)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 7 x \cdot x + 5 y (- 5 y)$

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

Move $x$ .

$7 \cdot 7 (x \cdot x) + 5 y (- 5 y)$

Multiply $x$ by $x$ .

$7 \cdot 7 x^{2} + 5 y (- 5 y)$

Multiply $7$ by $7$ .

$49 x^{2} + 5 y (- 5 y)$

Rewrite using the commutative property of multiplication.

$49 x^{2} + 5 \cdot - 5 y \cdot y$

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

Move $y$ .

$49 x^{2} + 5 \cdot - 5 (y \cdot y)$

Multiply $y$ by $y$ .

$49 x^{2} + 5 \cdot - 5 y^{2}$

Multiply $5$ by $- 5$ .

$49 x^{2} - 25 y^{2}$