Algebra Examples

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

Step 1

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

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Step 1.1

Move $a$ .

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

Step 1.2

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

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Step 1.2.1

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

$- 3 (a^{1} a^{2}) b^{3} (4 b^{2})$

Step 1.2.2

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

$- 3 a^{1 + 2} b^{3} (4 b^{2})$

Step 1.3

Add $1$ and $2$ .

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

Step 2

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

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Step 2.1

Move $b^{2}$ .

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

Step 2.2

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

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

Step 2.3

Add $2$ and $3$ .

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

Step 3

Multiply $4$ by $- 3$ .

$- 12 a^{3} b^{5}$