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

Let's simplify the expression step by step:

The expression is \((16−12)^2 + 5(8 + 2^2)5^3 − (1 + 4)^2\).

1. Calculate each part:
- \(16 - 12 = 4\)
- \((4)^2 = 16\)

2. Now consider \(5(8 + 2^2)5^3\):
- \(2^2 = 4\)
- \(8 + 4 = 12\)
- Therefore, \(5(12)5^3\):
- First calculate \(5^3 = 125\):
- So, \(5(12)(125) = 60 * 125 = 7500\)

3. Now consider \((1 + 4)^2\):
- \(1 + 4 = 5\)
- So, \((5)^2 = 25\)

4. Put it all together:
- \(16 + 7500 - 25 = 16 + 7500 - 25 = 7491\)

Thus, the simplified numerator is:

\(\boxed{7491}\)

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