Algebra Examples

$\frac{a}{2} (6 a + 4 b - 3)$

Step 1

Apply the distributive property.

$\frac{a}{2} (6 a) + \frac{a}{2} (4 b) + \frac{a}{2} \cdot - 3$

Step 2

Simplify.

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Step 2.1

Rewrite using the commutative property of multiplication.

$6 \frac{a}{2} a + \frac{a}{2} (4 b) + \frac{a}{2} \cdot - 3$

Step 2.2

Rewrite using the commutative property of multiplication.

$6 \frac{a}{2} a + 4 \frac{a}{2} b + \frac{a}{2} \cdot - 3$

Step 2.3

Combine $\frac{a}{2}$ and $- 3$ .

$6 \frac{a}{2} a + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3

Simplify each term.

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Step 3.1

Cancel the common factor of $2$ .

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Step 3.1.1

Factor $2$ out of $6$ .

$2 (3) \frac{a}{2} a + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3.1.2

Cancel the common factor.

$2 \cdot 3 \frac{a}{2} a + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3.1.3

Rewrite the expression.

$3 a \cdot a + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3.2

Multiply $a$ by $a$ by adding the exponents.

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Step 3.2.1

Move $a$ .

$3 (a \cdot a) + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3.2.2

Multiply $a$ by $a$ .

$3 a^{2} + 4 \frac{a}{2} b + \frac{a \cdot - 3}{2}$

Step 3.3

Cancel the common factor of $2$ .

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Step 3.3.1

Factor $2$ out of $4$ .

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

Step 3.3.2

Cancel the common factor.

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

Step 3.3.3

Rewrite the expression.

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

Step 3.4

Move $- 3$ to the left of $a$ .

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

Step 3.5

Move the negative in front of the fraction.

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