Algebra Examples

$V = 5 a \cdot 2 a \cdot (a^{3} - 3 a^{2} + a)$

Step 1

Remove parentheses.

$V = 5 a \cdot (2 a) \cdot (a^{3} - 3 a^{2} + a)$

Step 2

Simplify $5 a \cdot (2 a) \cdot (a^{3} - 3 a^{2} + a)$ .

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Step 2.1

Multiply $a$ by $a$ by adding the exponents.

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Step 2.1.1

Move $a$ .

$V = 5 (a \cdot a) \cdot 2 \cdot (a^{3} - 3 a^{2} + a)$

Step 2.1.2

Multiply $a$ by $a$ .

$V = 5 a^{2} \cdot 2 \cdot (a^{3} - 3 a^{2} + a)$

Step 2.2

Multiply $2$ by $5$ .

$V = 10 a^{2} \cdot (a^{3} - 3 a^{2} + a)$

Step 2.3

Apply the distributive property.

$V = 10 a^{2} a^{3} + 10 a^{2} (- 3 a^{2}) + 10 a^{2} a$

Step 2.4

Simplify.

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Step 2.4.1

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

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Step 2.4.1.1

Move $a^{3}$ .

$V = 10 (a^{3} a^{2}) + 10 a^{2} (- 3 a^{2}) + 10 a^{2} a$

Step 2.4.1.2

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

$V = 10 a^{3 + 2} + 10 a^{2} (- 3 a^{2}) + 10 a^{2} a$

Step 2.4.1.3

Add $3$ and $2$ .

$V = 10 a^{5} + 10 a^{2} (- 3 a^{2}) + 10 a^{2} a$

Step 2.4.2

Rewrite using the commutative property of multiplication.

$V = 10 a^{5} + 10 \cdot - 3 a^{2} a^{2} + 10 a^{2} a$

Step 2.4.3

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

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Step 2.4.3.1

Move $a$ .

$V = 10 a^{5} + 10 \cdot - 3 a^{2} a^{2} + 10 (a \cdot a^{2})$

Step 2.4.3.2

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

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Step 2.4.3.2.1

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

$V = 10 a^{5} + 10 \cdot - 3 a^{2} a^{2} + 10 (a^{1} a^{2})$

Step 2.4.3.2.2

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

$V = 10 a^{5} + 10 \cdot - 3 a^{2} a^{2} + 10 a^{1 + 2}$

Step 2.4.3.3

Add $1$ and $2$ .

$V = 10 a^{5} + 10 \cdot - 3 a^{2} a^{2} + 10 a^{3}$

Step 2.5

Simplify each term.

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Step 2.5.1

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

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Step 2.5.1.1

Move $a^{2}$ .

$V = 10 a^{5} + 10 \cdot - 3 (a^{2} a^{2}) + 10 a^{3}$

Step 2.5.1.2

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

$V = 10 a^{5} + 10 \cdot - 3 a^{2 + 2} + 10 a^{3}$

Step 2.5.1.3

Add $2$ and $2$ .

$V = 10 a^{5} + 10 \cdot - 3 a^{4} + 10 a^{3}$

Step 2.5.2

Multiply $10$ by $- 3$ .

$V = 10 a^{5} - 30 a^{4} + 10 a^{3}$