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

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

Step 1

Apply the distributive property.

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

Step 2

Simplify.

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

Move $x^{2}$ .

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

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

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

$2 (x^{2} x^{1}) + 2 x (3 x) + 2 x \cdot 4$

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

$2 x^{2 + 1} + 2 x (3 x) + 2 x \cdot 4$

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $2$ .

$2 x^{3} + 2 \cdot 3 x \cdot x + 8 x$

Step 3

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$2 x^{3} + 2 \cdot 3 (x \cdot x) + 8 x$

Multiply $x$ by $x$ .

$2 x^{3} + 2 \cdot 3 x^{2} + 8 x$

Multiply $2$ by $3$ .

$2 x^{3} + 6 x^{2} + 8 x$