Simplify 1/3*(x^2(12x^2-9x+1))

$\frac{1}{3} \cdot (x^{2} (12 x^{2} - 9 x + 1))$

Step 1

Apply the distributive property.

$\frac{1}{3} \cdot (x^{2} (12 x^{2}) + x^{2} (- 9 x) + x^{2} \cdot 1)$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$\frac{1}{3} \cdot (12 x^{2} x^{2} + x^{2} (- 9 x) + x^{2} \cdot 1)$

Rewrite using the commutative property of multiplication.

$\frac{1}{3} \cdot (12 x^{2} x^{2} - 9 x^{2} x + x^{2} \cdot 1)$

Multiply $x^{2}$ by $1$ .

$\frac{1}{3} \cdot (12 x^{2} x^{2} - 9 x^{2} x + x^{2})$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$\frac{1}{3} \cdot (12 (x^{2} x^{2}) - 9 x^{2} x + x^{2})$

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

$\frac{1}{3} \cdot (12 x^{2 + 2} - 9 x^{2} x + x^{2})$

Add $2$ and $2$ .

$\frac{1}{3} \cdot (12 x^{4} - 9 x^{2} x + x^{2})$

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

Move $x$ .

$\frac{1}{3} \cdot (12 x^{4} - 9 (x \cdot x^{2}) + x^{2})$

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

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

$\frac{1}{3} \cdot (12 x^{4} - 9 (x^{1} x^{2}) + x^{2})$

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

$\frac{1}{3} \cdot (12 x^{4} - 9 x^{1 + 2} + x^{2})$

Add $1$ and $2$ .

$\frac{1}{3} \cdot (12 x^{4} - 9 x^{3} + x^{2})$

Step 4

Apply the distributive property.

$\frac{1}{3} (12 x^{4}) + \frac{1}{3} (- 9 x^{3}) + \frac{1}{3} x^{2}$

Step 5

Simplify.

Cancel the common factor of $3$ .

Factor $3$ out of $12 x^{4}$ .

$\frac{1}{3} (3 (4 x^{4})) + \frac{1}{3} (- 9 x^{3}) + \frac{1}{3} x^{2}$

Cancel the common factor.

$\frac{1}{3} (3 (4 x^{4})) + \frac{1}{3} (- 9 x^{3}) + \frac{1}{3} x^{2}$

Rewrite the expression.

$4 x^{4} + \frac{1}{3} (- 9 x^{3}) + \frac{1}{3} x^{2}$

Cancel the common factor of $3$ .

Factor $3$ out of $- 9 x^{3}$ .

$4 x^{4} + \frac{1}{3} (3 (- 3 x^{3})) + \frac{1}{3} x^{2}$

Cancel the common factor.

$4 x^{4} + \frac{1}{3} (3 (- 3 x^{3})) + \frac{1}{3} x^{2}$

Rewrite the expression.

$4 x^{4} - 3 x^{3} + \frac{1}{3} x^{2}$

Combine $\frac{1}{3}$ and $x^{2}$ .

$4 x^{4} - 3 x^{3} + \frac{x^{2}}{3}$

Simplify 1/3*(x^2(12x^2-9x+1))

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