Algebra Examples

$(- 3 b^{2}) (- 2 b + b^{2} c)$

Step 1

Apply the distributive property.

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

Step 2

Rewrite using the commutative property of multiplication.

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

Step 3

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

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Step 3.1

Move $b^{2}$ .

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

Step 3.2

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

$- 3 \cdot - 2 b^{2} b - 3 b^{2 + 2} c$

Step 3.3

Add $2$ and $2$ .

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

Step 4

Simplify each term.

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Step 4.1

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

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Step 4.1.1

Move $b$ .

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

Step 4.1.2

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

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Step 4.1.2.1

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

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

Step 4.1.2.2

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

$- 3 \cdot - 2 b^{1 + 2} - 3 b^{4} c$

Step 4.1.3

Add $1$ and $2$ .

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

Step 4.2

Multiply $- 3$ by $- 2$ .

$6 b^{3} - 3 b^{4} c$