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

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

Expand $(x - 4) (- 2 x^{2} - 3 x + 4)$ by multiplying each term in the first expression by each term in the second expression.

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

Simplify terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x^{2}$ .

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

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

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

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

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

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

Add $2$ and $1$ .

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

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $4$ to the left of $x$ .

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

Multiply $- 2$ by $- 4$ .

$- 2 x^{3} - 3 x^{2} + 4 x + 8 x^{2} - 4 (- 3 x) - 4 \cdot 4$

Multiply $- 3$ by $- 4$ .

$- 2 x^{3} - 3 x^{2} + 4 x + 8 x^{2} + 12 x - 4 \cdot 4$

Multiply $- 4$ by $4$ .

$- 2 x^{3} - 3 x^{2} + 4 x + 8 x^{2} + 12 x - 16$

Simplify by adding terms.

Add $- 3 x^{2}$ and $8 x^{2}$ .

$- 2 x^{3} + 5 x^{2} + 4 x + 12 x - 16$

Add $4 x$ and $12 x$ .

$- 2 x^{3} + 5 x^{2} + 16 x - 16$