Simplify 2u(6u^2-9uv+v^2)

$2 u (6 u^{2} - 9 u v + v^{2})$

Step 1

Apply the distributive property.

$2 u (6 u^{2}) + 2 u (- 9 u v) + 2 u v^{2}$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$2 \cdot 6 u \cdot u^{2} + 2 u (- 9 u v) + 2 u v^{2}$

Multiply $u$ by $u$ by adding the exponents.

Move $u$ .

$2 \cdot 6 u \cdot u^{2} + 2 (u \cdot u) (- 9 v) + 2 u v^{2}$

Multiply $u$ by $u$ .

$2 \cdot 6 u \cdot u^{2} + 2 u^{2} (- 9 v) + 2 u v^{2}$

Step 3

Simplify each term.

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

Move $u^{2}$ .

$2 \cdot 6 (u^{2} u) + 2 u^{2} (- 9 v) + 2 u v^{2}$

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

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

$2 \cdot 6 (u^{2} u^{1}) + 2 u^{2} (- 9 v) + 2 u v^{2}$

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

$2 \cdot 6 u^{2 + 1} + 2 u^{2} (- 9 v) + 2 u v^{2}$

Add $2$ and $1$ .

$2 \cdot 6 u^{3} + 2 u^{2} (- 9 v) + 2 u v^{2}$

Multiply $2$ by $6$ .

$12 u^{3} + 2 u^{2} (- 9 v) + 2 u v^{2}$

Rewrite using the commutative property of multiplication.

$12 u^{3} + 2 \cdot - 9 u^{2} v + 2 u v^{2}$

Multiply $2$ by $- 9$ .

$12 u^{3} - 18 u^{2} v + 2 u v^{2}$