Basic Math Examples

$\frac{1}{2} \cdot (8 a^{2} - 10 a + 5)$

Step 1

Apply the distributive property.

$\frac{1}{2} (8 a^{2}) + \frac{1}{2} (- 10 a) + \frac{1}{2} \cdot 5$

Step 2

Simplify.

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Step 2.1

Cancel the common factor of $2$ .

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Step 2.1.1

Factor $2$ out of $8 a^{2}$ .

$\frac{1}{2} (2 (4 a^{2})) + \frac{1}{2} (- 10 a) + \frac{1}{2} \cdot 5$

Step 2.1.2

Cancel the common factor.

$\frac{1}{2} (2 (4 a^{2})) + \frac{1}{2} (- 10 a) + \frac{1}{2} \cdot 5$

Step 2.1.3

Rewrite the expression.

$4 a^{2} + \frac{1}{2} (- 10 a) + \frac{1}{2} \cdot 5$

Step 2.2

Cancel the common factor of $2$ .

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Step 2.2.1

Factor $2$ out of $- 10 a$ .

$4 a^{2} + \frac{1}{2} (2 (- 5 a)) + \frac{1}{2} \cdot 5$

Step 2.2.2

Cancel the common factor.

$4 a^{2} + \frac{1}{2} (2 (- 5 a)) + \frac{1}{2} \cdot 5$

Step 2.2.3

Rewrite the expression.

$4 a^{2} - 5 a + \frac{1}{2} \cdot 5$

Step 2.3

Combine $\frac{1}{2}$ and $5$ .

$4 a^{2} - 5 a + \frac{5}{2}$