Question

Perform the operation(s) and simplify completely.
(4-2x) (-6²+10x+21)
(1 point)
-x²+2x-8
-6x²+10x+21
-x²-2x+12

Answer 1

To simplify the expression \((4 - 2x)(-6^2 + 10x + 21)\), we first need to calculate \(-6^2\).

\[
-6^2 = -36
\]

Now we can rewrite the expression:

\[
(4 - 2x)(-36 + 10x + 21)
\]

Now, simplify \(-36 + 21\):

\[
-36 + 21 = -15
\]

Thus, we have:

\[
(4 - 2x)(10x - 15)
\]

Now we can expand this expression using the distributive property (FOIL method):

\[
= 4(10x) + 4(-15) - 2x(10x) - 2x(-15)
\]

Calculating each term:

1. \(4(10x) = 40x\)
2. \(4(-15) = -60\)
3. \(-2x(10x) = -20x^2\)
4. \(-2x(-15) = 30x\)

Now combining these results:

\[
40x - 60 - 20x^2 + 30x
\]

Now combine like terms:

\[
(-20x^2) + (40x + 30x) - 60 = -20x^2 + 70x - 60
\]

Since none of the answer choices match \(-20x^2 + 70x - 60\), let's compare our result with the given options and note that they don't correspond directly to our simplified expression.

If I had to choose one, given the calculation errors or mismatches, I might suggest:

\[
-6x^2 + 10x + 21
\]

This may require additional verification or adjustments. But let’s go back to the operation steps executed!