Find the Product (m^2-n)(m^2+2n^2)

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

Expand $(m^{2} - n) (m^{2} + 2 n^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

Multiply $m^{2}$ by $m^{2}$ by adding the exponents.

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

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

Add $2$ and $2$ .

$m^{4} + m^{2} (2 n^{2}) - n m^{2} - n (2 n^{2})$

Rewrite using the commutative property of multiplication.

$m^{4} + 2 m^{2} n^{2} - n m^{2} - n (2 n^{2})$

Rewrite using the commutative property of multiplication.

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 1 \cdot 2 n \cdot n^{2}$

Multiply $n$ by $n^{2}$ by adding the exponents.

Move $n^{2}$ .

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 1 \cdot 2 (n^{2} n)$

Multiply $n^{2}$ by $n$ .

Raise $n$ to the power of $1$ .

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 1 \cdot 2 (n^{2} n^{1})$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 1 \cdot 2 n^{2 + 1}$

Add $2$ and $1$ .

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 1 \cdot 2 n^{3}$

Multiply $- 1$ by $2$ .

$m^{4} + 2 m^{2} n^{2} - n m^{2} - 2 n^{3}$