Algebra Examples

$- 5 a b \cdot (a^{2} - 2 b)$

Step 1

Apply the distributive property.

$- 5 a b a^{2} - 5 a b (- 2 b)$

Step 2

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

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Step 2.1

Move $a^{2}$ .

$- 5 (a^{2} a) b - 5 a b (- 2 b)$

Step 2.2

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

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Step 2.2.1

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

$- 5 (a^{2} a^{1}) b - 5 a b (- 2 b)$

Step 2.2.2

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

$- 5 a^{2 + 1} b - 5 a b (- 2 b)$

Step 2.3

Add $2$ and $1$ .

$- 5 a^{3} b - 5 a b (- 2 b)$

Step 3

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

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Step 3.1

Move $b$ .

$- 5 a^{3} b - 5 a (b \cdot b) \cdot - 2$

Step 3.2

Multiply $b$ by $b$ .

$- 5 a^{3} b - 5 a b^{2} \cdot - 2$

Step 4

Multiply $- 2$ by $- 5$ .

$- 5 a^{3} b + 10 a b^{2}$