Algebra Examples

$- 4 b (1 - 9 b - 2 b^{2})$

Step 1

Apply the distributive property.

$- 4 b \cdot 1 - 4 b (- 9 b) - 4 b (- 2 b^{2})$

Step 2

Simplify.

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Step 2.1

Multiply $- 4$ by $1$ .

$- 4 b - 4 b (- 9 b) - 4 b (- 2 b^{2})$

Step 2.2

Rewrite using the commutative property of multiplication.

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

Step 2.3

Rewrite using the commutative property of multiplication.

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

Step 3

Simplify each term.

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Step 3.1

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

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Step 3.1.1

Move $b$ .

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

Step 3.1.2

Multiply $b$ by $b$ .

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

Step 3.2

Multiply $- 4$ by $- 9$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 b \cdot b^{2}$

Step 3.3

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

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Step 3.3.1

Move $b^{2}$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 (b^{2} b)$

Step 3.3.2

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

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Step 3.3.2.1

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

$- 4 b + 36 b^{2} - 4 \cdot - 2 (b^{2} b^{1})$

Step 3.3.2.2

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

$- 4 b + 36 b^{2} - 4 \cdot - 2 b^{2 + 1}$

Step 3.3.3

Add $2$ and $1$ .

$- 4 b + 36 b^{2} - 4 \cdot - 2 b^{3}$

Step 3.4

Multiply $- 4$ by $- 2$ .

$- 4 b + 36 b^{2} + 8 b^{3}$