Pre-Algebra Examples

$\frac{63 b^{4} - 9 b^{3}}{- 9 b}$

Step 1

Factor $9 b^{3}$ out of $63 b^{4} - 9 b^{3}$ .

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Step 1.1

Factor $9 b^{3}$ out of $63 b^{4}$ .

$\frac{9 b^{3} (7 b) - 9 b^{3}}{- 9 b}$

Step 1.2

Factor $9 b^{3}$ out of $- 9 b^{3}$ .

$\frac{9 b^{3} (7 b) + 9 b^{3} (- 1)}{- 9 b}$

Step 1.3

Factor $9 b^{3}$ out of $9 b^{3} (7 b) + 9 b^{3} (- 1)$ .

$\frac{9 b^{3} (7 b - 1)}{- 9 b}$

Step 2

Cancel the common factor of $9$ and $- 9$ .

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Step 2.1

Factor $9$ out of $9 b^{3} (7 b - 1)$ .

$\frac{9 (b^{3} (7 b - 1))}{- 9 b}$

Step 2.2

Cancel the common factors.

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Step 2.2.1

Factor $9$ out of $- 9 b$ .

$\frac{9 (b^{3} (7 b - 1))}{9 (- b)}$

Step 2.2.2

Cancel the common factor.

$\frac{9 (b^{3} (7 b - 1))}{9 (- b)}$

Step 2.2.3

Rewrite the expression.

$\frac{b^{3} (7 b - 1)}{- b}$

Step 3

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

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Step 3.1

Factor $b$ out of $b^{3} (7 b - 1)$ .

$\frac{b (b^{2} (7 b - 1))}{- b}$

Step 3.2

Move the negative one from the denominator of $\frac{b^{2} (7 b - 1)}{- 1}$ .

$- 1 \cdot (b^{2} (7 b - 1))$

Step 4

Rewrite $- 1 \cdot (b^{2} (7 b - 1))$ as $- (b^{2} (7 b - 1))$ .

$- (b^{2} (7 b - 1))$

Step 5

Apply the distributive property.

$- (b^{2} (7 b) + b^{2} \cdot - 1)$

Step 6

Rewrite using the commutative property of multiplication.

$- (7 b^{2} b + b^{2} \cdot - 1)$

Step 7

Move $- 1$ to the left of $b^{2}$ .

$- (7 b^{2} b - 1 \cdot b^{2})$

Step 8

Simplify each term.

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Step 8.1

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

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Step 8.1.1

Move $b$ .

$- (7 (b \cdot b^{2}) - 1 \cdot b^{2})$

Step 8.1.2

Multiply $b$ by $b^{2}$ .

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Step 8.1.2.1

Raise $b$ to the power of $1$ .

$- (7 (b^{1} b^{2}) - 1 \cdot b^{2})$

Step 8.1.2.2

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

$- (7 b^{1 + 2} - 1 \cdot b^{2})$

Step 8.1.3

Add $1$ and $2$ .

$- (7 b^{3} - 1 \cdot b^{2})$

Step 8.2

Rewrite $- 1 b^{2}$ as $- b^{2}$ .

$- (7 b^{3} - b^{2})$

Step 9

Apply the distributive property.

$- (7 b^{3}) - - b^{2}$

Step 10

Multiply $7$ by $- 1$ .

$- 7 b^{3} - - b^{2}$

Step 11

Multiply $- - b^{2}$ .

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Step 11.1

Multiply $- 1$ by $- 1$ .

$- 7 b^{3} + 1 b^{2}$

Step 11.2

Multiply $b^{2}$ by $1$ .

$- 7 b^{3} + b^{2}$