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

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

Step 1

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

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

Step 2

Expand $(3 m - 2 n^{2}) (3 m - 2 n^{2})$ using the FOIL Method.

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Step 3

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $m$ .

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

Multiply $m$ by $m$ .

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

Multiply $3$ by $3$ .

$9 m^{2} + 3 m (- 2 n^{2}) - 2 n^{2} (3 m) - 2 n^{2} (- 2 n^{2})$

Rewrite using the commutative property of multiplication.

$9 m^{2} + 3 \cdot - 2 m n^{2} - 2 n^{2} (3 m) - 2 n^{2} (- 2 n^{2})$

Multiply $3$ by $- 2$ .

$9 m^{2} - 6 m n^{2} - 2 n^{2} (3 m) - 2 n^{2} (- 2 n^{2})$

Rewrite using the commutative property of multiplication.

$9 m^{2} - 6 m n^{2} - 2 \cdot 3 n^{2} m - 2 n^{2} (- 2 n^{2})$

Multiply $- 2$ by $3$ .

$9 m^{2} - 6 m n^{2} - 6 n^{2} m - 2 n^{2} (- 2 n^{2})$

Rewrite using the commutative property of multiplication.

$9 m^{2} - 6 m n^{2} - 6 n^{2} m - 2 \cdot - 2 n^{2} n^{2}$

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

Move $n^{2}$ .

$9 m^{2} - 6 m n^{2} - 6 n^{2} m - 2 \cdot - 2 (n^{2} n^{2})$

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

$9 m^{2} - 6 m n^{2} - 6 n^{2} m - 2 \cdot - 2 n^{2 + 2}$

Add $2$ and $2$ .

$9 m^{2} - 6 m n^{2} - 6 n^{2} m - 2 \cdot - 2 n^{4}$

Multiply $- 2$ by $- 2$ .

$9 m^{2} - 6 m n^{2} - 6 n^{2} m + 4 n^{4}$

Subtract $6 n^{2} m$ from $- 6 m n^{2}$ .

Move $n^{2}$ .

$9 m^{2} - 6 m n^{2} - 6 m n^{2} + 4 n^{4}$

Subtract $6 m n^{2}$ from $- 6 m n^{2}$ .

$9 m^{2} - 12 m n^{2} + 4 n^{4}$

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

Related Questions

Support LCMGCF.com by disabling your adblocker.