Simplify (mn+1)(m^2n-1)(mn^2+2)

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

Expand $(m n + 1) (m^{2} n - 1)$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify each term.

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

Move $m^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

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

Move $n$ .

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

Multiply $n$ by $n$ .

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

Move $- 1$ to the left of $m n$ .

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

Rewrite $- 1 (m n)$ as $- (m n)$ .

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

Multiply $m^{2} n$ by $1$ .

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

Multiply $- 1$ by $1$ .

$(m^{3} n^{2} - m n + m^{2} n - 1) (m n^{2} + 2)$

Expand $(m^{3} n^{2} - m n + m^{2} n - 1) (m n^{2} + 2)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify each term.

Multiply $m^{3}$ by $m$ by adding the exponents.

Move $m$ .

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

Multiply $m$ by $m^{3}$ .

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

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

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

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

Add $1$ and $3$ .

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

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

Move $n^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Move $2$ to the left of $m^{3} n^{2}$ .

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

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

Move $m$ .

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

Multiply $m$ by $m$ .

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

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

Move $n^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Multiply $2$ by $- 1$ .

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

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

Move $m$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

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

Move $n^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Move $2$ to the left of $m^{2} n$ .

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

Rewrite $- 1 (m n^{2})$ as $- (m n^{2})$ .

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

Multiply $- 1$ by $2$ .

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

Simplify (mn+1)(m^2n-1)(mn^2+2)

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