Simplify (m+7n)(m-7n)

$(m + 7 n) (m - 7 n)$

Step 1

Expand $(m + 7 n) (m - 7 n)$ using the FOIL Method.

Apply the distributive property.

$m (m - 7 n) + 7 n (m - 7 n)$

Apply the distributive property.

$m \cdot m + m (- 7 n) + 7 n (m - 7 n)$

Apply the distributive property.

$m \cdot m + m (- 7 n) + 7 n m + 7 n (- 7 n)$

Step 2

Simplify terms.

Combine the opposite terms in $m \cdot m + m (- 7 n) + 7 n m + 7 n (- 7 n)$ .

Reorder the factors in the terms $m (- 7 n)$ and $7 n m$ .

$m \cdot m - 7 m n + 7 m n + 7 n (- 7 n)$

Add $- 7 m n$ and $7 m n$ .

$m \cdot m + 0 + 7 n (- 7 n)$

Add $m \cdot m$ and $0$ .

$m \cdot m + 7 n (- 7 n)$

Simplify each term.

Multiply $m$ by $m$ .

$m^{2} + 7 n (- 7 n)$

Rewrite using the commutative property of multiplication.

$m^{2} + 7 \cdot - 7 n \cdot n$

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

Move $n$ .

$m^{2} + 7 \cdot - 7 (n \cdot n)$

Multiply $n$ by $n$ .

$m^{2} + 7 \cdot - 7 n^{2}$

Multiply $7$ by $- 7$ .

$m^{2} - 49 n^{2}$