What is the value of `2^2+6^2+10^2+14^2-1^2-5^2-9^2-13^2`?

Options

A. 0
B. 15
C. 30
D. 60

Answer

To solve the expression \(2^2 + 6^2 + 10^2 + 14^2 - 1^2 - 5^2 - 9^2 - 13^2\), we can break it down step by step.

### Step 1: Calculate the squares of each number
First, we will calculate the squares of the numbers involved in the expression.

- \(2^2 = 4\)
- \(6^2 = 36\)
- \(10^2 = 100\)
- \(14^2 = 196\)
- \(1^2 = 1\)
- \(5^2 = 25\)
- \(9^2 = 81\)
- \(13^2 = 169\)

### Step 2: Substitute the squares back into the expression
Now we substitute these values back into the expression:

\[ 4 + 36 + 100 + 196 - 1 - 25 - 81 - 169 \]

### Step 3: Group the positive and negative terms
Next, we can group the positive and negative terms:

Positive terms:
\[ 4 + 36 + 100 + 196 = 336 \]

Negative terms:
\[ 1 + 25 + 81 + 169 = 276 \]

### Step 4: Subtract the sum of negative terms from the sum of positive terms
Now we subtract the sum of the negative terms from the sum of the positive terms:

\[ 336 - 276 = 60 \]

### Final Answer
Thus, the value of the expression \(2^2 + 6^2 + 10^2 + 14^2 - 1^2 - 5^2 - 9^2 - 13^2\) is \(60\).

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