Simplify 2a(a^4+a^2)

$2 a (a^{4} + a^{2})$

Step 1

Apply the distributive property.

$2 a \cdot a^{4} + 2 a \cdot a^{2}$

Step 2

Multiply $a$ by $a^{4}$ by adding the exponents.

Move $a^{4}$ .

$2 (a^{4} a) + 2 a \cdot a^{2}$

Multiply $a^{4}$ by $a$ .

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

$2 (a^{4} a^{1}) + 2 a \cdot a^{2}$

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

$2 a^{4 + 1} + 2 a \cdot a^{2}$

Add $4$ and $1$ .

$2 a^{5} + 2 a \cdot a^{2}$

Step 3

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

Move $a^{2}$ .

$2 a^{5} + 2 (a^{2} a)$

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

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

$2 a^{5} + 2 (a^{2} a^{1})$

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

$2 a^{5} + 2 a^{2 + 1}$

Add $2$ and $1$ .

$2 a^{5} + 2 a^{3}$