Simplify 3x^2-5x^3-x(2x^2+4x)

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

Simplify each term.

Apply the distributive property.

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

Rewrite using the commutative property of multiplication.

$3 x^{2} - 5 x^{3} - 1 \cdot 2 x \cdot x^{2} - x (4 x)$

Rewrite using the commutative property of multiplication.

$3 x^{2} - 5 x^{3} - 1 \cdot 2 x \cdot x^{2} - 1 \cdot 4 x \cdot x$

Simplify each term.

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

Move $x^{2}$ .

$3 x^{2} - 5 x^{3} - 1 \cdot 2 (x^{2} x) - 1 \cdot 4 x \cdot x$

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

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

$3 x^{2} - 5 x^{3} - 1 \cdot 2 (x^{2} x^{1}) - 1 \cdot 4 x \cdot x$

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

$3 x^{2} - 5 x^{3} - 1 \cdot 2 x^{2 + 1} - 1 \cdot 4 x \cdot x$

Add $2$ and $1$ .

$3 x^{2} - 5 x^{3} - 1 \cdot 2 x^{3} - 1 \cdot 4 x \cdot x$

Multiply $- 1$ by $2$ .

$3 x^{2} - 5 x^{3} - 2 x^{3} - 1 \cdot 4 x \cdot x$

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

Move $x$ .

$3 x^{2} - 5 x^{3} - 2 x^{3} - 1 \cdot 4 (x \cdot x)$

Multiply $x$ by $x$ .

$3 x^{2} - 5 x^{3} - 2 x^{3} - 1 \cdot 4 x^{2}$

Multiply $- 1$ by $4$ .

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

Simplify by adding terms.

Subtract $4 x^{2}$ from $3 x^{2}$ .

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

Subtract $2 x^{3}$ from $- 5 x^{3}$ .

$- 7 x^{3} - x^{2}$