Simplify 2x^2(x^3+x^2+4x)

$2 x^{2} (x^{3} + x^{2} + 4 x)$

Apply the distributive property.

$2 x^{2} x^{3} + 2 x^{2} x^{2} + 2 x^{2} (4 x)$

Simplify.

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

Move $x^{3}$ .

$2 (x^{3} x^{2}) + 2 x^{2} x^{2} + 2 x^{2} (4 x)$

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

$2 x^{3 + 2} + 2 x^{2} x^{2} + 2 x^{2} (4 x)$

Add $3$ and $2$ .

$2 x^{5} + 2 x^{2} x^{2} + 2 x^{2} (4 x)$

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

Move $x^{2}$ .

$2 x^{5} + 2 (x^{2} x^{2}) + 2 x^{2} (4 x)$

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

$2 x^{5} + 2 x^{2 + 2} + 2 x^{2} (4 x)$

Add $2$ and $2$ .

$2 x^{5} + 2 x^{4} + 2 x^{2} (4 x)$

Rewrite using the commutative property of multiplication.

$2 x^{5} + 2 x^{4} + 2 \cdot 4 x^{2} x$

Simplify each term.

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

Move $x$ .

$2 x^{5} + 2 x^{4} + 2 \cdot 4 (x \cdot x^{2})$

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

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

$2 x^{5} + 2 x^{4} + 2 \cdot 4 (x^{1} x^{2})$

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

$2 x^{5} + 2 x^{4} + 2 \cdot 4 x^{1 + 2}$

Add $1$ and $2$ .

$2 x^{5} + 2 x^{4} + 2 \cdot 4 x^{3}$

Multiply $2$ by $4$ .

$2 x^{5} + 2 x^{4} + 8 x^{3}$