Basic Math Examples

$4 a^{3} b^{2} (a^{2} c - 3 a b - 10 a^{3} b^{3})$

Step 1

Factor.

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Step 1.1

Factor $- a$ out of $a^{2} c - 3 a b - 10 a^{3} b^{3}$ .

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Step 1.1.1

Reorder the expression.

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Step 1.1.1.1

Move $- 3 a b$ .

$4 a^{3} b^{2} (a^{2} c - 10 a^{3} b^{3} - 3 a b)$

Step 1.1.1.2

Reorder $a^{2} c$ and $- 10 a^{3} b^{3}$ .

$4 a^{3} b^{2} (- 10 a^{3} b^{3} + a^{2} c - 3 a b)$

Step 1.1.2

Factor $- a$ out of $- 10 a^{3} b^{3}$ .

$4 a^{3} b^{2} (- a (10 a^{2} b^{3}) + a^{2} c - 3 a b)$

Step 1.1.3

Factor $- a$ out of $a^{2} c$ .

$4 a^{3} b^{2} (- a (10 a^{2} b^{3}) - a (- a c) - 3 a b)$

Step 1.1.4

Factor $- a$ out of $- 3 a b$ .

$4 a^{3} b^{2} (- a (10 a^{2} b^{3}) - a (- a c) - a (3 b))$

Step 1.1.5

Factor $- a$ out of $- a (10 a^{2} b^{3}) - a (- a c)$ .

$4 a^{3} b^{2} (- a (10 a^{2} b^{3} - a c) - a (3 b))$

Step 1.1.6

Factor $- a$ out of $- a (10 a^{2} b^{3} - a c) - a (3 b)$ .

$4 a^{3} b^{2} (- a (10 a^{2} b^{3} - a c + 3 b))$

Step 1.2

Remove unnecessary parentheses.

$4 a^{3} b^{2} \cdot - 1 a (10 a^{2} b^{3} - a c + 3 b)$

Step 2

Combine exponents.

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Step 2.1

Factor out negative.

$- (4 a^{3} b^{2} a (10 a^{2} b^{3} - a c + 3 b))$

Step 2.2

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

$- (4 (a^{1} a^{3}) b^{2} (10 a^{2} b^{3} - a c + 3 b))$

Step 2.3

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

$- (4 a^{1 + 3} b^{2} (10 a^{2} b^{3} - a c + 3 b))$

Step 2.4

Add $1$ and $3$ .

$- (4 a^{4} b^{2} (10 a^{2} b^{3} - a c + 3 b))$

Step 2.5

Multiply $4$ by $- 1$ .

$- 4 (a^{4} b^{2} (10 a^{2} b^{3} - a c + 3 b))$

Step 3

Remove unnecessary parentheses.

$- 4 a^{4} b^{2} (10 a^{2} b^{3} - a c + 3 b)$