Algebra Examples

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

Step 1

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

Tap for more steps...

Step 1.1

Move $a$ .

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

Step 1.2

Multiply $a$ by $a$ .

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

Step 2

Multiply $2$ by $5$ .

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

Step 3

Apply the distributive property.

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

Step 4

Simplify.

Tap for more steps...

Step 4.1

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

Tap for more steps...

Step 4.1.1

Move $a^{3}$ .

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

Step 4.1.2

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

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

Step 4.1.3

Add $3$ and $2$ .

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

Step 4.2

Rewrite using the commutative property of multiplication.

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

Step 4.3

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

Tap for more steps...

Step 4.3.1

Move $a$ .

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

Step 4.3.2

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

Tap for more steps...

Step 4.3.2.1

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

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

Step 4.3.2.2

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

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

Step 4.3.3

Add $1$ and $2$ .

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

Step 5

Simplify each term.

Tap for more steps...

Step 5.1

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

Tap for more steps...

Step 5.1.1

Move $a^{2}$ .

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

Step 5.1.2

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

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

Step 5.1.3

Add $2$ and $2$ .

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

Step 5.2

Multiply $10$ by $- 3$ .

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