Consider the expression (16−12)2+5(8+22)53−(1+4)2

Question

(
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.