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:
- \(4(10x) = 40x\)
- \(4(-15) = -60\)
- \(-2x(10x) = -20x^2\)
- \(-2x(-15) = 30x\)
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!
1 answer