Pre-Algebra Examples

$\frac{27 b^{10} + 3 b^{6} - 6 b^{4}}{3 b^{2}}$

Step 1

Factor $3 b^{4}$ out of $27 b^{10} + 3 b^{6} - 6 b^{4}$ .

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Step 1.1

Factor $3 b^{4}$ out of $27 b^{10}$ .

$\frac{3 b^{4} (9 b^{6}) + 3 b^{6} - 6 b^{4}}{3 b^{2}}$

Step 1.2

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

$\frac{3 b^{4} (9 b^{6}) + 3 b^{4} (b^{2}) - 6 b^{4}}{3 b^{2}}$

Step 1.3

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

$\frac{3 b^{4} (9 b^{6}) + 3 b^{4} (b^{2}) + 3 b^{4} (- 2)}{3 b^{2}}$

Step 1.4

Factor $3 b^{4}$ out of $3 b^{4} (9 b^{6}) + 3 b^{4} (b^{2})$ .

$\frac{3 b^{4} (9 b^{6} + b^{2}) + 3 b^{4} (- 2)}{3 b^{2}}$

Step 1.5

Factor $3 b^{4}$ out of $3 b^{4} (9 b^{6} + b^{2}) + 3 b^{4} (- 2)$ .

$\frac{3 b^{4} (9 b^{6} + b^{2} - 2)}{3 b^{2}}$

Step 2

Cancel the common factor of $3$ .

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Step 2.1

Cancel the common factor.

$\frac{3 b^{4} (9 b^{6} + b^{2} - 2)}{3 b^{2}}$

Step 2.2

Rewrite the expression.

$\frac{b^{4} (9 b^{6} + b^{2} - 2)}{b^{2}}$

Step 3

Cancel the common factor of $b^{4}$ and $b^{2}$ .

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Step 3.1

Factor $b^{2}$ out of $b^{4} (9 b^{6} + b^{2} - 2)$ .

$\frac{b^{2} (b^{2} (9 b^{6} + b^{2} - 2))}{b^{2}}$

Step 3.2

Cancel the common factors.

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Step 3.2.1

Multiply by $1$ .

$\frac{b^{2} (b^{2} (9 b^{6} + b^{2} - 2))}{b^{2} \cdot 1}$

Step 3.2.2

Cancel the common factor.

$\frac{b^{2} (b^{2} (9 b^{6} + b^{2} - 2))}{b^{2} \cdot 1}$

Step 3.2.3

Rewrite the expression.

$\frac{b^{2} (9 b^{6} + b^{2} - 2)}{1}$

Step 3.2.4

Divide $b^{2} (9 b^{6} + b^{2} - 2)$ by $1$ .

$b^{2} (9 b^{6} + b^{2} - 2)$

Step 4

Apply the distributive property.

$b^{2} (9 b^{6}) + b^{2} b^{2} + b^{2} \cdot - 2$

Step 5

Simplify.

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Step 5.1

Rewrite using the commutative property of multiplication.

$9 b^{2} b^{6} + b^{2} b^{2} + b^{2} \cdot - 2$

Step 5.2

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

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Step 5.2.1

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

$9 b^{2} b^{6} + b^{2 + 2} + b^{2} \cdot - 2$

Step 5.2.2

Add $2$ and $2$ .

$9 b^{2} b^{6} + b^{4} + b^{2} \cdot - 2$

Step 5.3

Move $- 2$ to the left of $b^{2}$ .

$9 b^{2} b^{6} + b^{4} - 2 \cdot b^{2}$

Step 6

Multiply $b^{2}$ by $b^{6}$ by adding the exponents.

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Step 6.1

Move $b^{6}$ .

$9 (b^{6} b^{2}) + b^{4} - 2 \cdot b^{2}$

Step 6.2

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

$9 b^{6 + 2} + b^{4} - 2 \cdot b^{2}$

Step 6.3

Add $6$ and $2$ .

$9 b^{8} + b^{4} - 2 \cdot b^{2}$

$9 b^{8} + b^{4} - 2 b^{2}$