Question
Perform the operation(s) and simplify completely.
(4−2x)(−6x2+10x+214−2x)
(1 point)
Responses
−x3+5x2−6x+3
negative x cubed plus 5 x squared minus 6 x plus 3
−6x2+10x+21
negative 6 x squared plus 10 x plus 21
−x2−2x+12
negative x squared minus 2 x plus 12
−x2+2x−8
negative x squared plus 2 x minus 8
(4−2x)(−6x2+10x+214−2x)
(1 point)
Responses
−x3+5x2−6x+3
negative x cubed plus 5 x squared minus 6 x plus 3
−6x2+10x+21
negative 6 x squared plus 10 x plus 21
−x2−2x+12
negative x squared minus 2 x plus 12
−x2+2x−8
negative x squared plus 2 x minus 8
Answers
GPT-4o mini
To perform the operation and simplify \((4 - 2x)(-6x^2 + 10x + 21 - 2x)\), we start by simplifying the expression inside the parentheses.
1. Combine the like terms in \(-6x^2 + 10x + 21 - 2x\):
\[
-6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21
\]
Next, substitute this back into the original expression:
\[
(4 - 2x)(-6x^2 + 8x + 21)
\]
2. Now, we will distribute \((4 - 2x)\) across \((-6x^2 + 8x + 21)\):
\[
= 4(-6x^2) + 4(8x) + 4(21) - 2x(-6x^2) - 2x(8x) - 2x(21)
\]
This expands to:
\[
= -24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x
\]
3. Now, combine the like terms:
\[
12x^3 + (-24x^2 - 16x^2) + (32x - 42x) + 84
\]
\[
= 12x^3 - 40x^2 - 10x + 84
\]
The fully simplified expression is:
\[
12x^3 - 40x^2 - 10x + 84
\]
There seems to be no option that matches directly to our final answer, but let's verify:
- None of the responses provided:
- \(-x^3 + 5x^2 - 6x + 3\)
- \(-6x^2 + 10x + 21\)
- \(-x^2 - 2x + 12\)
- \(-x^2 + 2x - 8\)
...matches the calculated result of \(12x^3 - 40x^2 - 10x + 84\).
If you need to check any specific queries or calculations, feel free to let me know!
1. Combine the like terms in \(-6x^2 + 10x + 21 - 2x\):
\[
-6x^2 + (10x - 2x) + 21 = -6x^2 + 8x + 21
\]
Next, substitute this back into the original expression:
\[
(4 - 2x)(-6x^2 + 8x + 21)
\]
2. Now, we will distribute \((4 - 2x)\) across \((-6x^2 + 8x + 21)\):
\[
= 4(-6x^2) + 4(8x) + 4(21) - 2x(-6x^2) - 2x(8x) - 2x(21)
\]
This expands to:
\[
= -24x^2 + 32x + 84 + 12x^3 - 16x^2 - 42x
\]
3. Now, combine the like terms:
\[
12x^3 + (-24x^2 - 16x^2) + (32x - 42x) + 84
\]
\[
= 12x^3 - 40x^2 - 10x + 84
\]
The fully simplified expression is:
\[
12x^3 - 40x^2 - 10x + 84
\]
There seems to be no option that matches directly to our final answer, but let's verify:
- None of the responses provided:
- \(-x^3 + 5x^2 - 6x + 3\)
- \(-6x^2 + 10x + 21\)
- \(-x^2 - 2x + 12\)
- \(-x^2 + 2x - 8\)
...matches the calculated result of \(12x^3 - 40x^2 - 10x + 84\).
If you need to check any specific queries or calculations, feel free to let me know!