Find the Product (2m-3n)(m-5n)

$(2 m - 3 n) (m - 5 n)$

Step 1

Expand $(2 m - 3 n) (m - 5 n)$ using the FOIL Method.

Apply the distributive property.

$2 m (m - 5 n) - 3 n (m - 5 n)$

Apply the distributive property.

$2 m \cdot m + 2 m (- 5 n) - 3 n (m - 5 n)$

Apply the distributive property.

$2 m \cdot m + 2 m (- 5 n) - 3 n m - 3 n (- 5 n)$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $m$ .

$2 (m \cdot m) + 2 m (- 5 n) - 3 n m - 3 n (- 5 n)$

Multiply $m$ by $m$ .

$2 m^{2} + 2 m (- 5 n) - 3 n m - 3 n (- 5 n)$

Rewrite using the commutative property of multiplication.

$2 m^{2} + 2 \cdot - 5 m n - 3 n m - 3 n (- 5 n)$

Multiply $2$ by $- 5$ .

$2 m^{2} - 10 m n - 3 n m - 3 n (- 5 n)$

Rewrite using the commutative property of multiplication.

$2 m^{2} - 10 m n - 3 n m - 3 \cdot - 5 n \cdot n$

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

Move $n$ .

$2 m^{2} - 10 m n - 3 n m - 3 \cdot - 5 (n \cdot n)$

Multiply $n$ by $n$ .

$2 m^{2} - 10 m n - 3 n m - 3 \cdot - 5 n^{2}$

Multiply $- 3$ by $- 5$ .

$2 m^{2} - 10 m n - 3 n m + 15 n^{2}$

Subtract $3 n m$ from $- 10 m n$ .

Move $n$ .

$2 m^{2} - 10 m n - 3 m n + 15 n^{2}$

Subtract $3 m n$ from $- 10 m n$ .

$2 m^{2} - 13 m n + 15 n^{2}$