Find the Product (m^3-8n)^2

${(m^{3} - 8 n)}^{2}$

Rewrite ${(m^{3} - 8 n)}^{2}$ as $(m^{3} - 8 n) (m^{3} - 8 n)$ .

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

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

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

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

Add $3$ and $3$ .

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

Rewrite using the commutative property of multiplication.

$m^{6} - 8 m^{3} n - 8 n m^{3} - 8 n (- 8 n)$

Rewrite using the commutative property of multiplication.

$m^{6} - 8 m^{3} n - 8 n m^{3} - 8 \cdot - 8 n \cdot n$

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

Move $n$ .

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

Multiply $n$ by $n$ .

$m^{6} - 8 m^{3} n - 8 n m^{3} - 8 \cdot - 8 n^{2}$

Multiply $- 8$ by $- 8$ .

$m^{6} - 8 m^{3} n - 8 n m^{3} + 64 n^{2}$

Subtract $8 n m^{3}$ from $- 8 m^{3} n$ .

Move $n$ .

$m^{6} - 8 m^{3} n - 8 m^{3} n + 64 n^{2}$

Subtract $8 m^{3} n$ from $- 8 m^{3} n$ .

$m^{6} - 16 m^{3} n + 64 n^{2}$