Basic Math Examples

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

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$\frac{1}{2} (2 a) + \frac{1}{2} b - (4 a + b)$

Step 1.2

Cancel the common factor of $2$ .

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Step 1.2.1

Factor $2$ out of $2 a$ .

$\frac{1}{2} (2 (a)) + \frac{1}{2} b - (4 a + b)$

Step 1.2.2

Cancel the common factor.

$\frac{1}{2} (2 a) + \frac{1}{2} b - (4 a + b)$

Step 1.2.3

Rewrite the expression.

$a + \frac{1}{2} b - (4 a + b)$

$a + \frac{1}{2} b - (4 a + b)$

Step 1.3

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

$a + \frac{b}{2} - (4 a + b)$

Step 1.4

Apply the distributive property.

$a + \frac{b}{2} - (4 a) - b$

Step 1.5

Multiply $4$ by $- 1$ .

$a + \frac{b}{2} - 4 a - b$

$a + \frac{b}{2} - 4 a - b$

Step 2

Subtract $4 a$ from $a$ .

$- 3 a + \frac{b}{2} - b$

Step 3

To write $- b$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$- 3 a + \frac{b}{2} - b \cdot \frac{2}{2}$

Step 4

Simplify terms.

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Step 4.1

Combine $- b$ and $\frac{2}{2}$ .

$- 3 a + \frac{b}{2} + \frac{- b \cdot 2}{2}$

Step 4.2

Combine the numerators over the common denominator.

$- 3 a + \frac{b - b \cdot 2}{2}$

$- 3 a + \frac{b - b \cdot 2}{2}$

Step 5

Simplify each term.

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Step 5.1

Simplify the numerator.

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Step 5.1.1

Factor $b$ out of $b - b \cdot 2$ .

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Step 5.1.1.1

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

$- 3 a + \frac{b^{1} - b \cdot 2}{2}$

Step 5.1.1.2

Factor $b$ out of $b^{1}$ .

$- 3 a + \frac{b \cdot 1 - b \cdot 2}{2}$

Step 5.1.1.3

Factor $b$ out of $- b \cdot 2$ .

$- 3 a + \frac{b \cdot 1 + b (- 1 \cdot 2)}{2}$

Step 5.1.1.4

Factor $b$ out of $b \cdot 1 + b (- 1 \cdot 2)$ .

$- 3 a + \frac{b (1 - 1 \cdot 2)}{2}$

$- 3 a + \frac{b (1 - 1 \cdot 2)}{2}$

Step 5.1.2

Multiply $- 1$ by $2$ .

$- 3 a + \frac{b (1 - 2)}{2}$

Step 5.1.3

Subtract $2$ from $1$ .

$- 3 a + \frac{b \cdot - 1}{2}$

$- 3 a + \frac{b \cdot - 1}{2}$

Step 5.2

Move $- 1$ to the left of $b$ .

$- 3 a + \frac{- 1 \cdot b}{2}$

Step 5.3

Move the negative in front of the fraction.

$- 3 a - \frac{b}{2}$

$- 3 a - \frac{b}{2}$

$[\begin{array}{c} x^{2} & \frac{1}{2} \\ \sqrt{π} & \int x d x \end{array}]$