Basic Math Examples

$(6 A) + (6 B) - 36 = (A - 6) \cdot (B - 6)$

Step 1

Simplify $(A - 6) \cdot (B - 6)$ .

Tap for more steps...

Step 1.1

Rewrite.

$6 A + 6 B - 36 = 0 + 0 + (A - 6) \cdot (B - 6)$

Step 1.2

Simplify by adding zeros.

$6 A + 6 B - 36 = (A - 6) \cdot (B - 6)$

Step 1.3

Expand $(A - 6) (B - 6)$ using the FOIL Method.

Tap for more steps...

Step 1.3.1

Apply the distributive property.

$6 A + 6 B - 36 = A (B - 6) - 6 (B - 6)$

Step 1.3.2

Apply the distributive property.

$6 A + 6 B - 36 = A B + A \cdot - 6 - 6 (B - 6)$

Step 1.3.3

Apply the distributive property.

$6 A + 6 B - 36 = A B + A \cdot - 6 - 6 B - 6 \cdot - 6$

Step 1.4

Simplify each term.

Tap for more steps...

Step 1.4.1

Move $- 6$ to the left of $A$ .

$6 A + 6 B - 36 = A B - 6 \cdot A - 6 B - 6 \cdot - 6$

Step 1.4.2

Multiply $- 6$ by $- 6$ .

$6 A + 6 B - 36 = A B - 6 A - 6 B + 36$

Step 2

Since $B$ is on the right side of the equation, switch the sides so it is on the left side of the equation.

$A B - 6 A - 6 B + 36 = 6 A + 6 B - 36$

Step 3

Move all terms containing $B$ to the left side of the equation.

Tap for more steps...

Step 3.1

Subtract $6 B$ from both sides of the equation.

$A B - 6 A - 6 B + 36 - 6 B = 6 A - 36$

Step 3.2

Subtract $6 B$ from $- 6 B$ .

$A B - 6 A - 12 B + 36 = 6 A - 36$

Step 4

Move all terms not containing $B$ to the right side of the equation.

Tap for more steps...

Step 4.1

Add $6 A$ to both sides of the equation.

$A B - 12 B + 36 = 6 A - 36 + 6 A$

Step 4.2

Subtract $36$ from both sides of the equation.

$A B - 12 B = 6 A - 36 + 6 A - 36$

Step 4.3

Add $6 A$ and $6 A$ .

$A B - 12 B = 12 A - 36 - 36$

Step 4.4

Subtract $36$ from $- 36$ .

$A B - 12 B = 12 A - 72$

Step 5

Factor $B$ out of $A B - 12 B$ .

Tap for more steps...

Step 5.1

Factor $B$ out of $A B$ .

$B A - 12 B = 12 A - 72$

Step 5.2

Factor $B$ out of $- 12 B$ .

$B A + B \cdot - 12 = 12 A - 72$

Step 5.3

Factor $B$ out of $B A + B \cdot - 12$ .

$B (A - 12) = 12 A - 72$

Step 6

Divide each term in $B (A - 12) = 12 A - 72$ by $A - 12$ and simplify.

Tap for more steps...

Step 6.1

Divide each term in $B (A - 12) = 12 A - 72$ by $A - 12$ .

$\frac{B (A - 12)}{A - 12} = \frac{12 A}{A - 12} + \frac{- 72}{A - 12}$

Step 6.2

Simplify the left side.

Tap for more steps...

Step 6.2.1

Cancel the common factor of $A - 12$ .

Tap for more steps...

Step 6.2.1.1

Cancel the common factor.

$\frac{B (A - 12)}{A - 12} = \frac{12 A}{A - 12} + \frac{- 72}{A - 12}$

Step 6.2.1.2

Divide $B$ by $1$ .

$B = \frac{12 A}{A - 12} + \frac{- 72}{A - 12}$

Step 6.3

Simplify the right side.

Tap for more steps...

Step 6.3.1

Combine the numerators over the common denominator.

$B = \frac{12 A - 72}{A - 12}$

Step 6.3.2

Factor $12$ out of $12 A - 72$ .

Tap for more steps...

Step 6.3.2.1

Factor $12$ out of $12 A$ .

$B = \frac{12 (A) - 72}{A - 12}$

Step 6.3.2.2

Factor $12$ out of $- 72$ .

$B = \frac{12 A + 12 \cdot - 6}{A - 12}$

Step 6.3.2.3

Factor $12$ out of $12 A + 12 \cdot - 6$ .

$B = \frac{12 (A - 6)}{A - 12}$