Algebra Examples

$12 (\frac{a}{3} - \frac{b}{4}) + 2 a - 6 b$

Step 1

Simplify each term.

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Step 1.1

Apply the distributive property.

$12 \frac{a}{3} + 12 (- \frac{b}{4}) + 2 a - 6 b$

Step 1.2

Cancel the common factor of $3$ .

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Step 1.2.1

Factor $3$ out of $12$ .

$3 (4) \frac{a}{3} + 12 (- \frac{b}{4}) + 2 a - 6 b$

Step 1.2.2

Cancel the common factor.

$3 \cdot 4 \frac{a}{3} + 12 (- \frac{b}{4}) + 2 a - 6 b$

Step 1.2.3

Rewrite the expression.

$4 a + 12 (- \frac{b}{4}) + 2 a - 6 b$

Step 1.3

Cancel the common factor of $4$ .

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Step 1.3.1

Move the leading negative in $- \frac{b}{4}$ into the numerator.

$4 a + 12 \frac{- b}{4} + 2 a - 6 b$

Step 1.3.2

Factor $4$ out of $12$ .

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

Step 1.3.3

Cancel the common factor.

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

Step 1.3.4

Rewrite the expression.

$4 a + 3 (- b) + 2 a - 6 b$

Step 1.4

Multiply $- 1$ by $3$ .

$4 a - 3 b + 2 a - 6 b$

Step 2

Simplify by adding terms.

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Step 2.1

Add $4 a$ and $2 a$ .

$6 a - 3 b - 6 b$

Step 2.2

Subtract $6 b$ from $- 3 b$ .

$6 a - 9 b$