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

100
100

76

Answer 1

To simplify the expression \((16−12)^2+5(8+22)53−(1+4)^2\), we'll break it down step by step.

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

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

3. Now evaluate \( 5(30)53 \):
- Assuming the expression means \( 5 \times 30 \times 53 \):
\[
5 \times 30 = 150
\]
Thus, taking \( 150 \times 53 \):
\[
150 \times 53 = 7950 \; (\text{this calculation will be checked stepwise next})
\]

First calculate \( 150 \times 53 \):
\[
150 \times 50 = 7500 \\
150 \times 3 = 450
\]
Adding these together:
\[
7500 + 450 = 7950
\]

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

Now, put all parts back into the expression:
\[
16 + 7950 - 25
\]

Calculate this step-by-step:
\[
16 + 7950 = 7966 \\
7966 - 25 = 7941
\]

Thus, the simplified numerator of the original expression is:
\[
\boxed{7941}
\]

This value is not among the given options, indicating there may be an error in the interpretation of the expression \(5(8+22)53\). Could you clarify the form of that term?