Simplify (m^3n+8)(m^3n-5)

$(m^{3} n + 8) (m^{3} n - 5)$

Step 1

Expand $(m^{3} n + 8) (m^{3} n - 5)$ using the FOIL Method.

Apply the distributive property.

$m^{3} n (m^{3} n - 5) + 8 (m^{3} n - 5)$

Apply the distributive property.

$m^{3} n (m^{3} n) + m^{3} n \cdot - 5 + 8 (m^{3} n - 5)$

Apply the distributive property.

$m^{3} n (m^{3} n) + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

Step 2

Simplify and combine like terms.

Simplify each term.

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

Move $m^{3}$ .

$m^{3} m^{3} n \cdot n + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

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

$m^{3 + 3} n \cdot n + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

Add $3$ and $3$ .

$m^{6} n \cdot n + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

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

Move $n$ .

$m^{6} (n \cdot n) + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

Multiply $n$ by $n$ .

$m^{6} n^{2} + m^{3} n \cdot - 5 + 8 (m^{3} n) + 8 \cdot - 5$

Move $- 5$ to the left of $m^{3} n$ .

$m^{6} n^{2} - 5 \cdot (m^{3} n) + 8 (m^{3} n) + 8 \cdot - 5$

Multiply $8$ by $- 5$ .

$m^{6} n^{2} - 5 m^{3} n + 8 m^{3} n - 40$

Add $- 5 m^{3} n$ and $8 m^{3} n$ .

$m^{6} n^{2} + 3 m^{3} n - 40$