Simplify 5a2a(a^3-3a^2+a)

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

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

Move $a$ .

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

Multiply $a$ by $a$ .

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

Multiply $2$ by $5$ .

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

Apply the distributive property.

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

Simplify.

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

Move $a^{3}$ .

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

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

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

Add $3$ and $2$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $a$ .

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

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

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

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

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

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

Add $1$ and $2$ .

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

Simplify each term.

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

Move $a^{2}$ .

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

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

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

Add $2$ and $2$ .

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

Multiply $10$ by $- 3$ .

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

Simplify 5a*2a*(a^3-3a^2+a)