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

. What is the simplified numerator?(1 point)
Responses

100
100

54
54

76
76

42+60

1 answer

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

  1. Calculate \( (16-12) \): \[ 16 - 12 = 4 \]

  2. Now calculate \( (16-12)^2 \): \[ 4^2 = 16 \]

  3. Next calculate \( (1 + 4) \): \[ 1 + 4 = 5 \]

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

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

  6. Now calculate \( 5(30)53 \). Here we interpret \( 53 \) to mean multiplication by \( 53 \): \[ 5 \times 30 \times 53 = 150 \times 53 \]

    We will calculate \( 150 \times 53 \) as follows: \[ 150 \times 53 = 150 \times (50 + 3) = 150 \times 50 + 150 \times 3 = 7500 + 450 = 7950 \]

  7. Now we can substitute these values into the original expression: \[ 16 + 7950 - 25 \]

  8. Now perform the addition and subtraction: \[ 16 - 25 = -9 \] \[ -9 + 7950 = 7941 \]

The simplified numerator of the expression is \( 7941 \).

Now, none of the given options (100, 54, 76, or \( 42 + 60 \)) match \( 7941 \). If those options were meant to match some part of the calculation, it might be unclear without further context. But based on the full evaluation, the result is \( 7941 \).