Find the Product (7m+8n)(7m-8n)

$(7 m + 8 n) (7 m - 8 n)$

Step 1

Expand $(7 m + 8 n) (7 m - 8 n)$ using the FOIL Method.

Apply the distributive property.

$7 m (7 m - 8 n) + 8 n (7 m - 8 n)$

Apply the distributive property.

$7 m (7 m) + 7 m (- 8 n) + 8 n (7 m - 8 n)$

Apply the distributive property.

$7 m (7 m) + 7 m (- 8 n) + 8 n (7 m) + 8 n (- 8 n)$

Step 2

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$7 \cdot 7 m \cdot m + 7 m (- 8 n) + 8 n (7 m) + 8 n (- 8 n)$

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

Move $m$ .

$7 \cdot 7 (m \cdot m) + 7 m (- 8 n) + 8 n (7 m) + 8 n (- 8 n)$

Multiply $m$ by $m$ .

$7 \cdot 7 m^{2} + 7 m (- 8 n) + 8 n (7 m) + 8 n (- 8 n)$

Multiply $7$ by $7$ .

$49 m^{2} + 7 m (- 8 n) + 8 n (7 m) + 8 n (- 8 n)$

Rewrite using the commutative property of multiplication.

$49 m^{2} + 7 \cdot - 8 m n + 8 n (7 m) + 8 n (- 8 n)$

Multiply $7$ by $- 8$ .

$49 m^{2} - 56 m n + 8 n (7 m) + 8 n (- 8 n)$

Rewrite using the commutative property of multiplication.

$49 m^{2} - 56 m n + 8 \cdot 7 n m + 8 n (- 8 n)$

Multiply $8$ by $7$ .

$49 m^{2} - 56 m n + 56 n m + 8 n (- 8 n)$

Rewrite using the commutative property of multiplication.

$49 m^{2} - 56 m n + 56 n m + 8 \cdot - 8 n \cdot n$

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

Move $n$ .

$49 m^{2} - 56 m n + 56 n m + 8 \cdot - 8 (n \cdot n)$

Multiply $n$ by $n$ .

$49 m^{2} - 56 m n + 56 n m + 8 \cdot - 8 n^{2}$

Multiply $8$ by $- 8$ .

$49 m^{2} - 56 m n + 56 n m - 64 n^{2}$

Add $- 56 m n$ and $56 n m$ .

Move $n$ .

$49 m^{2} - 56 m n + 56 m n - 64 n^{2}$

Add $- 56 m n$ and $56 m n$ .

$49 m^{2} + 0 - 64 n^{2}$

Add $49 m^{2}$ and $0$ .

$49 m^{2} - 64 n^{2}$