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

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

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

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

Move $- 3$ to the left of $x^{2}$ .

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

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

Move $x^{3}$ .

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

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

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

Add $3$ and $2$ .

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

$2 x^{5} - 3 x^{2} - 3 x (x + 4)$

Apply the distributive property.

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

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

Move $x$ .

$2 x^{5} - 3 x^{2} - 3 (x \cdot x) - 3 x \cdot 4$

Multiply $x$ by $x$ .

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

Multiply $4$ by $- 3$ .

$2 x^{5} - 3 x^{2} - 3 x^{2} - 12 x$

Subtract $3 x^{2}$ from $- 3 x^{2}$ .

$2 x^{5} - 6 x^{2} - 12 x$