Pre-Algebra Examples

$\frac{4 b^{6} - 4 b^{8} - 3 b^{11}}{b^{3}}$

Step 1

Factor $b^{6}$ out of $4 b^{6} - 4 b^{8} - 3 b^{11}$ .

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Step 1.1

Factor $b^{6}$ out of $4 b^{6}$ .

$\frac{b^{6} \cdot 4 - 4 b^{8} - 3 b^{11}}{b^{3}}$

Step 1.2

Factor $b^{6}$ out of $- 4 b^{8}$ .

$\frac{b^{6} \cdot 4 + b^{6} (- 4 b^{2}) - 3 b^{11}}{b^{3}}$

Step 1.3

Factor $b^{6}$ out of $- 3 b^{11}$ .

$\frac{b^{6} \cdot 4 + b^{6} (- 4 b^{2}) + b^{6} (- 3 b^{5})}{b^{3}}$

Step 1.4

Factor $b^{6}$ out of $b^{6} \cdot 4 + b^{6} (- 4 b^{2})$ .

$\frac{b^{6} \cdot (4 - 4 b^{2}) + b^{6} (- 3 b^{5})}{b^{3}}$

Step 1.5

Factor $b^{6}$ out of $b^{6} \cdot (4 - 4 b^{2}) + b^{6} (- 3 b^{5})$ .

$\frac{b^{6} (4 - 4 b^{2} - 3 b^{5})}{b^{3}}$

Step 2

Cancel the common factor of $b^{6}$ and $b^{3}$ .

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Step 2.1

Factor $b^{3}$ out of $b^{6} (4 - 4 b^{2} - 3 b^{5})$ .

$\frac{b^{3} (b^{3} (4 - 4 b^{2} - 3 b^{5}))}{b^{3}}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Multiply by $1$ .

$\frac{b^{3} (b^{3} (4 - 4 b^{2} - 3 b^{5}))}{b^{3} \cdot 1}$

Step 2.2.2

Cancel the common factor.

$\frac{b^{3} (b^{3} (4 - 4 b^{2} - 3 b^{5}))}{b^{3} \cdot 1}$

Step 2.2.3

Rewrite the expression.

$\frac{b^{3} (4 - 4 b^{2} - 3 b^{5})}{1}$

Step 2.2.4

Divide $b^{3} (4 - 4 b^{2} - 3 b^{5})$ by $1$ .

$b^{3} (4 - 4 b^{2} - 3 b^{5})$

Step 3

Apply the distributive property.

$b^{3} \cdot 4 + b^{3} (- 4 b^{2}) + b^{3} (- 3 b^{5})$

Step 4

Simplify.

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Step 4.1

Move $4$ to the left of $b^{3}$ .

$4 \cdot b^{3} + b^{3} (- 4 b^{2}) + b^{3} (- 3 b^{5})$

Step 4.2

Rewrite using the commutative property of multiplication.

$4 \cdot b^{3} - 4 b^{3} b^{2} + b^{3} (- 3 b^{5})$

Step 4.3

Rewrite using the commutative property of multiplication.

$4 \cdot b^{3} - 4 b^{3} b^{2} - 3 b^{3} b^{5}$

Step 5

Simplify each term.

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Step 5.1

Multiply $b^{3}$ by $b^{2}$ by adding the exponents.

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Step 5.1.1

Move $b^{2}$ .

$4 b^{3} - 4 (b^{2} b^{3}) - 3 b^{3} b^{5}$

Step 5.1.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 b^{3} - 4 b^{2 + 3} - 3 b^{3} b^{5}$

Step 5.1.3

Add $2$ and $3$ .

$4 b^{3} - 4 b^{5} - 3 b^{3} b^{5}$

Step 5.2

Multiply $b^{3}$ by $b^{5}$ by adding the exponents.

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Step 5.2.1

Move $b^{5}$ .

$4 b^{3} - 4 b^{5} - 3 (b^{5} b^{3})$

Step 5.2.2

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$4 b^{3} - 4 b^{5} - 3 b^{5 + 3}$

Step 5.2.3

Add $5$ and $3$ .

$4 b^{3} - 4 b^{5} - 3 b^{8}$