Basic Math Examples

$10 a^{3} + 15 a^{2} b + 8 a b^{2} \cdot (12 b^{3})$

Step 1

Factor $a$ out of $10 a^{3} + 15 a^{2} b + 8 a b^{2} \cdot (12 b^{3})$ .

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Step 1.1

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

$a (10 a^{2}) + 15 a^{2} b + 8 a b^{2} \cdot (12 b^{3})$

Step 1.2

Factor $a$ out of $15 a^{2} b$ .

$a (10 a^{2}) + a (15 a b) + 8 a b^{2} \cdot (12 b^{3})$

Step 1.3

Factor $a$ out of $8 a b^{2} \cdot (12 b^{3})$ .

$a (10 a^{2}) + a (15 a b) + a (8 b^{2} \cdot (12 b^{3}))$

Step 1.4

Factor $a$ out of $a (10 a^{2}) + a (15 a b)$ .

$a (10 a^{2} + 15 a b) + a (8 b^{2} \cdot (12 b^{3}))$

Step 1.5

Factor $a$ out of $a (10 a^{2} + 15 a b) + a (8 b^{2} \cdot (12 b^{3}))$ .

$a (10 a^{2} + 15 a b + 8 b^{2} \cdot (12 b^{3}))$

Step 2

Rewrite using the commutative property of multiplication.

$a (10 a^{2} + 15 a b + 8 \cdot 12 b^{2} b^{3})$

Step 3

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

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Step 3.1

Move $b^{3}$ .

$a (10 a^{2} + 15 a b + 8 \cdot 12 (b^{3} b^{2}))$

Step 3.2

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

$a (10 a^{2} + 15 a b + 8 \cdot 12 b^{3 + 2})$

Step 3.3

Add $3$ and $2$ .

$a (10 a^{2} + 15 a b + 8 \cdot 12 b^{5})$

Step 4

Multiply $8$ by $12$ .

$a (10 a^{2} + 15 a b + 96 b^{5})$