Perform the operation(s) and simplify completely.

Question

(4−2x)(−6x2+10x+214−2x)


(1 point)

Answer 1

To perform the operation and simplify the expression \((4-2x)(-6x^2 + 10x + 214 - 2x)\), we first simplify the expression inside the parentheses.

1. Combine like terms in the second part: \[ 10x - 2x = 8x \] So, we have: \[ -6x^2 + 8x + 214 \]

2. Now, we will distribute \((4 - 2x)\) with \((-6x^2 + 8x + 214)\): \[ (4 - 2x)(-6x^2 + 8x + 214) = 4(-6x^2) + 4(8x) + 4(214) - 2x(-6x^2) - 2x(8x) - 2x(214) \]

3. Now calculate each term:

   • \(4 \cdot -6x^2 = -24x^2\)
   • \(4 \cdot 8x = 32x\)
   • \(4 \cdot 214 = 856\)
   • \(-2x \cdot -6x^2 = 12x^3\)
   • \(-2x \cdot 8x = -16x^2\)
   • \(-2x \cdot 214 = -428x\)

4. Now combine all of these results: \[ 12x^3 + (-24x^2 - 16x^2) + (32x - 428x) + 856 \]

5. Combine like terms:

   • For \(x^3\) terms: \(12x^3\)
   • For \(x^2\) terms: \(-24x^2 - 16x^2 = -40x^2\)
   • For \(x\) terms: \(32x - 428x = -396x\)
   • The constant term is \(856\).

6. Putting it all together: \[ 12x^3 - 40x^2 - 396x + 856 \]

Thus, the completely simplified expression is: \[ \boxed{12x^3 - 40x^2 - 396x + 856} \]