Algebra Examples

$\frac{1}{2} \cdot (x^{2} (8 x^{2} - 6 x + 1))$

Step 1

Apply the distributive property.

$\frac{1}{2} \cdot (x^{2} (8 x^{2}) + x^{2} (- 6 x) + x^{2} \cdot 1)$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (8 x^{2} x^{2} + x^{2} (- 6 x) + x^{2} \cdot 1)$

Step 2.2

Rewrite using the commutative property of multiplication.

$\frac{1}{2} \cdot (8 x^{2} x^{2} - 6 x^{2} x + x^{2} \cdot 1)$

Step 2.3

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

$\frac{1}{2} \cdot (8 x^{2} x^{2} - 6 x^{2} x + x^{2})$

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $x^{2}$ .

$\frac{1}{2} \cdot (8 (x^{2} x^{2}) - 6 x^{2} x + x^{2})$

Step 3.1.2

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

$\frac{1}{2} \cdot (8 x^{2 + 2} - 6 x^{2} x + x^{2})$

Step 3.1.3

Add $2$ and $2$ .

$\frac{1}{2} \cdot (8 x^{4} - 6 x^{2} x + x^{2})$

Step 3.2

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

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Step 3.2.1

Move $x$ .

$\frac{1}{2} \cdot (8 x^{4} - 6 (x \cdot x^{2}) + x^{2})$

Step 3.2.2

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

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Step 3.2.2.1

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

$\frac{1}{2} \cdot (8 x^{4} - 6 (x^{1} x^{2}) + x^{2})$

Step 3.2.2.2

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

$\frac{1}{2} \cdot (8 x^{4} - 6 x^{1 + 2} + x^{2})$

Step 3.2.3

Add $1$ and $2$ .

$\frac{1}{2} \cdot (8 x^{4} - 6 x^{3} + x^{2})$

Step 4

Apply the distributive property.

$\frac{1}{2} (8 x^{4}) + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} x^{2}$

Step 5

Simplify.

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Step 5.1

Cancel the common factor of $2$ .

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Step 5.1.1

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

$\frac{1}{2} (2 (4 x^{4})) + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} x^{2}$

Step 5.1.2

Cancel the common factor.

$\frac{1}{2} (2 (4 x^{4})) + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} x^{2}$

Step 5.1.3

Rewrite the expression.

$4 x^{4} + \frac{1}{2} (- 6 x^{3}) + \frac{1}{2} x^{2}$

Step 5.2

Cancel the common factor of $2$ .

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Step 5.2.1

Factor $2$ out of $- 6 x^{3}$ .

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

Step 5.2.2

Cancel the common factor.

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

Step 5.2.3

Rewrite the expression.

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

Step 5.3

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

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