Simplify -2/3n^2(-9n^2+3n+6)

$- \frac{2}{3} n^{2} (- 9 n^{2} + 3 n + 6)$

Step 1

Apply the distributive property.

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

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

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

Rewrite using the commutative property of multiplication.

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

Move $6$ to the left of $n^{2}$ .

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

Step 3

Simplify each term.

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

Move $n^{2}$ .

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

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

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

Add $2$ and $2$ .

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 n^{2} n + 6 \cdot n^{2})$

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

Move $n$ .

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 (n \cdot n^{2}) + 6 \cdot n^{2})$

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

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

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 (n^{1} n^{2}) + 6 \cdot n^{2})$

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

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 n^{1 + 2} + 6 \cdot n^{2})$

Add $1$ and $2$ .

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 n^{3} + 6 \cdot n^{2})$

$- \frac{2}{3} \cdot (- 9 n^{4} + 3 n^{3} + 6 n^{2})$

Step 4

Apply the distributive property.

$- \frac{2}{3} (- 9 n^{4}) - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Step 5

Simplify.

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$\frac{- 2}{3} (- 9 n^{4}) - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Factor $3$ out of $- 9 n^{4}$ .

$\frac{- 2}{3} (3 (- 3 n^{4})) - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Cancel the common factor.

$\frac{- 2}{3} (3 (- 3 n^{4})) - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Rewrite the expression.

$- 2 (- 3 n^{4}) - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Multiply $- 3$ by $- 2$ .

$6 n^{4} - \frac{2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$6 n^{4} + \frac{- 2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Factor $3$ out of $3 n^{3}$ .

$6 n^{4} + \frac{- 2}{3} (3 (n^{3})) - \frac{2}{3} (6 n^{2})$

Cancel the common factor.

$6 n^{4} + \frac{- 2}{3} (3 n^{3}) - \frac{2}{3} (6 n^{2})$

Rewrite the expression.

$6 n^{4} - 2 n^{3} - \frac{2}{3} (6 n^{2})$

Cancel the common factor of $3$ .

Move the leading negative in $- \frac{2}{3}$ into the numerator.

$6 n^{4} - 2 n^{3} + \frac{- 2}{3} (6 n^{2})$

Factor $3$ out of $6 n^{2}$ .

$6 n^{4} - 2 n^{3} + \frac{- 2}{3} (3 (2 n^{2}))$

Cancel the common factor.

$6 n^{4} - 2 n^{3} + \frac{- 2}{3} (3 (2 n^{2}))$

Rewrite the expression.

$6 n^{4} - 2 n^{3} - 2 (2 n^{2})$

Multiply $2$ by $- 2$ .

$6 n^{4} - 2 n^{3} - 4 n^{2}$

Simplify -2/3n^2(-9n^2+3n+6)

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