Question

Consider the expression (16−12)2+5(8+22)53−(1+4)2. What is the simplified numerator?(1 point)
Responses

54
54

42+60
4 squared plus 60

76
76

100

Answer 1

To simplify the expression \((16−12)^2 + 5(8+22)53−(1+4)^2\), we will go step by step:

1. **Calculate \(16 - 12\):**
\[
16 - 12 = 4
\]
Then, we calculate \((4)^2\):
\[
(4)^2 = 16
\]

2. **Calculate \(8 + 22\):**
\[
8 + 22 = 30
\]

3. **Calculate \(5 \times 30 \times 53\):**
\[
5 \times 30 = 150
\]
Now we need to multiply by \(53\):
\[
150 \times 53 = 7950
\]

4. **Calculate \(1 + 4\):**
\[
1 + 4 = 5
\]
Then, we calculate \((5)^2\):
\[
(5)^2 = 25
\]

5. **Now put everything together:**
We have:
\[
16 + 7950 - 25
\]

6. **Calculate \(16 - 25\):**
\[
16 - 25 = -9
\]

7. **Finally, calculate \(-9 + 7950\):**
\[
7950 - 9 = 7941
\]

The simplified numerator of the expression is **7941**. However, this option does not appear in your responses.

If the question solely seeks the simplified expression before considering the effect of signs and arithmetic, the expression simplifies to \(16 + 7950 - 25\), which can also break down to \(16 - 25 + 5 \times (8 + 22) \times 53\).

Please clarify if "the simplified numerator" refers specifically to the calculation (the total) or one part of the expression, and perhaps check for any transcription errors in responses or the alternatives provided initially.