Expand the Trigonometric Expression (5m+2n)(5m-2n)

$(5 m + 2 n) (5 m - 2 n)$

Step 1

Expand $(5 m + 2 n) (5 m - 2 n)$ using the FOIL Method.

Apply the distributive property.

$5 m (5 m - 2 n) + 2 n (5 m - 2 n)$

Apply the distributive property.

$5 m (5 m) + 5 m (- 2 n) + 2 n (5 m - 2 n)$

Apply the distributive property.

$5 m (5 m) + 5 m (- 2 n) + 2 n (5 m) + 2 n (- 2 n)$

Step 2

Simplify terms.

Combine the opposite terms in $5 m (5 m) + 5 m (- 2 n) + 2 n (5 m) + 2 n (- 2 n)$ .

Reorder the factors in the terms $5 m (- 2 n)$ and $2 n (5 m)$ .

$5 m (5 m) - 2 \cdot 5 m n + 2 \cdot 5 m n + 2 n (- 2 n)$

Add $- 2 \cdot 5 m n$ and $2 \cdot 5 m n$ .

$5 m (5 m) + 0 + 2 n (- 2 n)$

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

$5 m (5 m) + 2 n (- 2 n)$

Simplify each term.

Rewrite using the commutative property of multiplication.

$5 \cdot 5 m \cdot m + 2 n (- 2 n)$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$5 \cdot 5 (m \cdot m) + 2 n (- 2 n)$

Multiply $m$ by $m$ .

$5 \cdot 5 m^{2} + 2 n (- 2 n)$

Multiply $5$ by $5$ .

$25 m^{2} + 2 n (- 2 n)$

Rewrite using the commutative property of multiplication.

$25 m^{2} + 2 \cdot - 2 n \cdot n$

Multiply $n$ by $n$ by adding the exponents.

Move $n$ .

$25 m^{2} + 2 \cdot - 2 (n \cdot n)$

Multiply $n$ by $n$ .

$25 m^{2} + 2 \cdot - 2 n^{2}$

Multiply $2$ by $- 2$ .

$25 m^{2} - 4 n^{2}$