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

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

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Multiply $4$ by $2$ .

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

Simplify each term.

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

Move $x^{2}$ .

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

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

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

$2 \cdot 3 (x^{2} x^{1}) + 8 x - 3 x^{2}$

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

$2 \cdot 3 x^{2 + 1} + 8 x - 3 x^{2}$

Add $2$ and $1$ .

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

Multiply $2$ by $3$ .

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

Move $8 x$ .

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