Question

Consider the expression (16−12)2+5(8+22)53−(1+4)2
(
16
−
12
)
2
+
5
(
8
+
2
2
)
5
3
−
(
1
+
4
)
2
. What is the simplified numerator?(1 point)
Responses

54
54

76
76

42+60
4
2
+
60
4 squared plus 60

100

Answer 1

To simplify the expression \((16−12)^2 + 5(8+2^2)5^3 − (1+4)^2\), we can break it down step by step.

1. Calculate \( (16 - 12)^2 \):
\[
16 - 12 = 4 \quad \Rightarrow \quad 4^2 = 16
\]

2. Calculate \( 2^2 \):
\[
2^2 = 4
\]
Now calculate \( 8 + 4 \):
\[
8 + 4 = 12
\]

3. Now, calculate \( 5(8 + 2^2) = 5(12) \):
\[
5 \times 12 = 60
\]

4. Calculate \( 5^3 \):
\[
5^3 = 125
\]

5. Now calculate \( 5(8+2^2)5^3 = 60 \times 125 \):
\[
60 \times 125 = 7500
\]

6. Now calculate \( (1 + 4)^2 \):
\[
1 + 4 = 5 \quad \Rightarrow \quad 5^2 = 25
\]

Now combine all the parts together:
\[
(16 - 12)^2 + 5(8 + 2^2)5^3 - (1 + 4)^2 = 16 + 7500 - 25
\]

Now perform the final calculation:
\[
16 + 7500 - 25 = 7500 + 16 - 25 = 7500 - 9 = 7491
\]

So the simplified numerator of the expression is **7491**.

None of the provided responses match this value (54, 76, \(42 + 60\), 100), therefore it appears these options are incorrect as they do not align with our calculations.