Basic Math Examples

$a = \frac{1}{2} \cdot (h (b (1 + b \cdot 2)))$

Step 1

Rewrite the equation as $\frac{1}{2} \cdot (h b (1 + b \cdot 2)) = a$ .

$\frac{1}{2} \cdot (h b (1 + b \cdot 2)) = a$

Step 2

Multiply both sides of the equation by $2$ .

$2 (\frac{1}{2} \cdot (h b (1 + b \cdot 2))) = 2 a$

Step 3

Simplify the left side.

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Step 3.1

Simplify $2 (\frac{1}{2} \cdot (h b (1 + b \cdot 2)))$ .

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Step 3.1.1

Move $2$ to the left of $b$ .

$2 (\frac{1}{2} \cdot (h b (1 + 2 b))) = 2 a$

Step 3.1.2

Simplify by multiplying through.

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Step 3.1.2.1

Apply the distributive property.

$2 (\frac{1}{2} \cdot (h b \cdot 1 + h b (2 b))) = 2 a$

Step 3.1.2.2

Simplify the expression.

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Step 3.1.2.2.1

Multiply $h$ by $1$ .

$2 (\frac{1}{2} \cdot (b \cdot h + h b (2 b))) = 2 a$

Step 3.1.2.2.2

Rewrite using the commutative property of multiplication.

$2 (\frac{1}{2} \cdot (b \cdot h + 2 h b \cdot b)) = 2 a$

Step 3.1.3

Multiply $b$ by $b$ by adding the exponents.

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Step 3.1.3.1

Move $b$ .

$2 (\frac{1}{2} \cdot (b h + 2 h (b \cdot b))) = 2 a$

Step 3.1.3.2

Multiply $b$ by $b$ .

$2 (\frac{1}{2} \cdot (b h + 2 h b^{2})) = 2 a$

Step 3.1.4

Apply the distributive property.

$2 (\frac{1}{2} (b h) + \frac{1}{2} (2 h b^{2})) = 2 a$

Step 3.1.5

Multiply $\frac{1}{2} (b h)$ .

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Step 3.1.5.1

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

$2 (\frac{b}{2} h + \frac{1}{2} (2 h b^{2})) = 2 a$

Step 3.1.5.2

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

$2 (\frac{b h}{2} + \frac{1}{2} (2 h b^{2})) = 2 a$

Step 3.1.6

Cancel the common factor of $2$ .

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Step 3.1.6.1

Factor $2$ out of $2 h b^{2}$ .

$2 (\frac{b h}{2} + \frac{1}{2} (2 (h b^{2}))) = 2 a$

Step 3.1.6.2

Cancel the common factor.

$2 (\frac{b h}{2} + \frac{1}{2} (2 (h b^{2}))) = 2 a$

Step 3.1.6.3

Rewrite the expression.

$2 (\frac{b h}{2} + h b^{2}) = 2 a$

Step 3.1.7

Apply the distributive property.

$2 \frac{b h}{2} + 2 (h b^{2}) = 2 a$

Step 3.1.8

Cancel the common factor of $2$ .

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Step 3.1.8.1

Cancel the common factor.

$2 \frac{b h}{2} + 2 (h b^{2}) = 2 a$

Step 3.1.8.2

Rewrite the expression.

$b h + 2 (h b^{2}) = 2 a$

$b h + 2 h b^{2} = 2 a$

Step 4

Factor $b h$ out of $b h + 2 h b^{2}$ .

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Step 4.1

Factor $b h$ out of $b h$ .

$b h (1) + 2 h b^{2} = 2 a$

Step 4.2

Factor $b h$ out of $2 h b^{2}$ .

$b h (1) + b h (2 b) = 2 a$

Step 4.3

Factor $b h$ out of $b h (1) + b h (2 b)$ .

$b h (1 + 2 b) = 2 a$

Step 5

Divide each term in $b h (1 + 2 b) = 2 a$ by $b (1 + 2 b)$ and simplify.

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Step 5.1

Divide each term in $b h (1 + 2 b) = 2 a$ by $b (1 + 2 b)$ .

$\frac{b h (1 + 2 b)}{b (1 + 2 b)} = \frac{2 a}{b (1 + 2 b)}$

Step 5.2

Simplify the left side.

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Step 5.2.1

Cancel the common factor of $b$ .

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Step 5.2.1.1

Cancel the common factor.

$\frac{b h (1 + 2 b)}{b (1 + 2 b)} = \frac{2 a}{b (1 + 2 b)}$

Step 5.2.1.2

Rewrite the expression.

$\frac{h (1 + 2 b)}{1 + 2 b} = \frac{2 a}{b (1 + 2 b)}$

Step 5.2.2

Cancel the common factor of $1 + 2 b$ .

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Step 5.2.2.1

Cancel the common factor.

$\frac{h (1 + 2 b)}{1 + 2 b} = \frac{2 a}{b (1 + 2 b)}$

Step 5.2.2.2

Divide $h$ by $1$ .

$h = \frac{2 a}{b (1 + 2 b)}$