Basic Math Examples

$a + 4 = \frac{1}{12} \cdot {(b + 3)}^{2}$

Step 1

Simplify $\frac{1}{12} \cdot {(b + 3)}^{2}$ .

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Step 1.1

Rewrite.

$a + 4 = 0 + 0 + \frac{1}{12} \cdot {(b + 3)}^{2}$

Step 1.2

Rewrite ${(b + 3)}^{2}$ as $(b + 3) (b + 3)$ .

$a + 4 = \frac{1}{12} \cdot ((b + 3) (b + 3))$

Step 1.3

Expand $(b + 3) (b + 3)$ using the FOIL Method.

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Step 1.3.1

Apply the distributive property.

$a + 4 = \frac{1}{12} \cdot (b (b + 3) + 3 (b + 3))$

Step 1.3.2

Apply the distributive property.

$a + 4 = \frac{1}{12} \cdot (b \cdot b + b \cdot 3 + 3 (b + 3))$

Step 1.3.3

Apply the distributive property.

$a + 4 = \frac{1}{12} \cdot (b \cdot b + b \cdot 3 + 3 b + 3 \cdot 3)$

Step 1.4

Simplify and combine like terms.

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Step 1.4.1

Simplify each term.

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Step 1.4.1.1

Multiply $b$ by $b$ .

$a + 4 = \frac{1}{12} \cdot (b^{2} + b \cdot 3 + 3 b + 3 \cdot 3)$

Step 1.4.1.2

Move $3$ to the left of $b$ .

$a + 4 = \frac{1}{12} \cdot (b^{2} + 3 \cdot b + 3 b + 3 \cdot 3)$

Step 1.4.1.3

Multiply $3$ by $3$ .

$a + 4 = \frac{1}{12} \cdot (b^{2} + 3 b + 3 b + 9)$

Step 1.4.2

Add $3 b$ and $3 b$ .

$a + 4 = \frac{1}{12} \cdot (b^{2} + 6 b + 9)$

Step 1.5

Apply the distributive property.

$a + 4 = \frac{1}{12} b^{2} + \frac{1}{12} (6 b) + \frac{1}{12} \cdot 9$

Step 1.6

Simplify.

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Step 1.6.1

Combine $\frac{1}{12}$ and $b^{2}$ .

$a + 4 = \frac{b^{2}}{12} + \frac{1}{12} (6 b) + \frac{1}{12} \cdot 9$

Step 1.6.2

Cancel the common factor of $6$ .

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Step 1.6.2.1

Factor $6$ out of $12$ .

$a + 4 = \frac{b^{2}}{12} + \frac{1}{6 (2)} (6 b) + \frac{1}{12} \cdot 9$

Step 1.6.2.2

Factor $6$ out of $6 b$ .

$a + 4 = \frac{b^{2}}{12} + \frac{1}{6 (2)} (6 (b)) + \frac{1}{12} \cdot 9$

Step 1.6.2.3

Cancel the common factor.

$a + 4 = \frac{b^{2}}{12} + \frac{1}{6 \cdot 2} (6 b) + \frac{1}{12} \cdot 9$

Step 1.6.2.4

Rewrite the expression.

$a + 4 = \frac{b^{2}}{12} + \frac{1}{2} b + \frac{1}{12} \cdot 9$

Step 1.6.3

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

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{1}{12} \cdot 9$

Step 1.6.4

Cancel the common factor of $3$ .

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Step 1.6.4.1

Factor $3$ out of $12$ .

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{1}{3 (4)} \cdot 9$

Step 1.6.4.2

Factor $3$ out of $9$ .

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{1}{3 \cdot 4} \cdot (3 \cdot 3)$

Step 1.6.4.3

Cancel the common factor.

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{1}{3 \cdot 4} \cdot (3 \cdot 3)$

Step 1.6.4.4

Rewrite the expression.

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{1}{4} \cdot 3$

Step 1.6.5

Combine $\frac{1}{4}$ and $3$ .

$a + 4 = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3}{4}$

Step 2

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

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Step 2.1

Subtract $4$ from both sides of the equation.

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3}{4} - 4$

Step 2.2

To write $- 4$ as a fraction with a common denominator, multiply by $\frac{4}{4}$ .

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3}{4} - 4 \cdot \frac{4}{4}$

Step 2.3

Combine $- 4$ and $\frac{4}{4}$ .

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3}{4} + \frac{- 4 \cdot 4}{4}$

Step 2.4

Combine the numerators over the common denominator.

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3 - 4 \cdot 4}{4}$

Step 2.5

Simplify the numerator.

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Step 2.5.1

Multiply $- 4$ by $4$ .

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{3 - 16}{4}$

Step 2.5.2

Subtract $16$ from $3$ .

$a = \frac{b^{2}}{12} + \frac{b}{2} + \frac{- 13}{4}$

Step 2.6

Move the negative in front of the fraction.

$a = \frac{b^{2}}{12} + \frac{b}{2} - \frac{13}{4}$