Pre-Algebra Examples

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

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

Step 1

Remove parentheses.

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

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

Step 2

Remove parentheses.

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

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

Step 3

Remove parentheses.

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

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

Step 4

Simplify

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

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

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Step 4.1

Move

2

$2$ to the left of

b

$b$ .

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

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

Step 4.2

Simplify by multiplying through.

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Step 4.2.1

Apply the distributive property.

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

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

Step 4.2.2

Simplify the expression.

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Step 4.2.2.1

Multiply

h

$h$ by

1

$1$ .

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

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

Step 4.2.2.2

Rewrite using the commutative property of multiplication.

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

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

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

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

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

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

Step 4.3

Multiply

b

$b$ by

b

$b$ by adding the exponents.

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Step 4.3.1

Move

b

$b$ .

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

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

Step 4.3.2

Multiply

b

$b$ by

b

$b$ .

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

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

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

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

Step 4.4

Apply the distributive property.

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

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

Step 4.5

Multiply

\frac{1}{2} (b h)

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

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Step 4.5.1

Combine

b

$b$ and

\frac{1}{2}

$\frac{1}{2}$ .

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

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

Step 4.5.2

Combine

\frac{b}{2}

$\frac{b}{2}$ and

h

$h$ .

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

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

Step 4.6

Cancel the common factor of

$2$ .

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Step 4.6.1

Factor

$2$ out of

$2 h b^{2}$ .

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

Step 4.6.2

Cancel the common factor.

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

Step 4.6.3

Rewrite the expression.

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

Step 4.7

Simplify with commuting.

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Step 4.7.1

Reorder

$h$ and

$b^{2}$ .

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

Step 4.7.2

Reorder

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

$b^{2} h$ .

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