Simplify 1/2*(x^2(8x^2-4x+1))

$\frac{1}{2} \cdot (x^{2} (8 x^{2} - 4 x + 1))$

Step 1

Apply the distributive property.

$\frac{1}{2} \cdot (x^{2} (8 x^{2}) + x^{2} (- 4 x) + x^{2} \cdot 1)$

Step 2

Simplify.

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (8 x^{2} x^{2} + x^{2} (- 4 x) + x^{2} \cdot 1)$

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (8 x^{2} x^{2} - 4 x^{2} x + x^{2} \cdot 1)$

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

$\frac{1}{2} \cdot (8 x^{2} x^{2} - 4 x^{2} x + x^{2})$

Step 3

Simplify each term.

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

Move $x^{2}$ .

$\frac{1}{2} \cdot (8 (x^{2} x^{2}) - 4 x^{2} x + x^{2})$

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

$\frac{1}{2} \cdot (8 x^{2 + 2} - 4 x^{2} x + x^{2})$

Add $2$ and $2$ .

$\frac{1}{2} \cdot (8 x^{4} - 4 x^{2} x + x^{2})$

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

Move $x$ .

$\frac{1}{2} \cdot (8 x^{4} - 4 (x \cdot x^{2}) + x^{2})$

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

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

$\frac{1}{2} \cdot (8 x^{4} - 4 (x^{1} x^{2}) + x^{2})$

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

$\frac{1}{2} \cdot (8 x^{4} - 4 x^{1 + 2} + x^{2})$

Add $1$ and $2$ .

$\frac{1}{2} \cdot (8 x^{4} - 4 x^{3} + x^{2})$

Step 4

Apply the distributive property.

$\frac{1}{2} (8 x^{4}) + \frac{1}{2} (- 4 x^{3}) + \frac{1}{2} x^{2}$

Step 5

Simplify.

Cancel the common factor of $2$ .

Factor $2$ out of $8 x^{4}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

Cancel the common factor of $2$ .

Factor $2$ out of $- 4 x^{3}$ .

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

Cancel the common factor.

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

Rewrite the expression.

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

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

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

Simplify 1/2*(x^2(8x^2-4x+1))

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