What is the value of `3^(2) + 7^(2) + 11^(2) + 13^(2) + 17^(2) - 1^(2) - 5^(2) - 9^(2) - 11^(2) - 15^(2)` ?

Options

A. 5
B. 72
C. 92
D. 184

Answer

To solve the expression \(3^{2} + 7^{2} + 11^{2} + 13^{2} + 17^{2} - 1^{2} - 5^{2} - 9^{2} - 11^{2} - 15^{2}\), we will break it down step by step.

### Step 1: Calculate the squares of the positive terms.
We will first calculate the squares of the numbers in the first part of the expression.

1. \(3^{2} = 9\)
2. \(7^{2} = 49\)
3. \(11^{2} = 121\)
4. \(13^{2} = 169\)
5. \(17^{2} = 289\)

Now, we can sum these values:
\[ 9 + 49 + 121 + 169 + 289 \]

### Step 2: Sum the squares of the positive terms.
Now we will add these values together:
\[ 9 + 49 = 58 \]
\[ 58 + 121 = 179 \]
\[ 179 + 169 = 348 \]
\[ 348 + 289 = 637 \]

### Step 3: Calculate the squares of the negative terms.
Next, we will calculate the squares of the numbers in the second part of the expression.

1. \(1^{2} = 1\)
2. \(5^{2} = 25\)
3. \(9^{2} = 81\)
4. \(11^{2} = 121\)
5. \(15^{2} = 225\)

Now, we can sum these values:
\[ 1 + 25 + 81 + 121 + 225 \]

### Step 4: Sum the squares of the negative terms.
Now we will add these values together:
\[ 1 + 25 = 26 \]
\[ 26 + 81 = 107 \]
\[ 107 + 121 = 228 \]
\[ 228 + 225 = 453 \]

### Step 5: Subtract the sum of the negative terms from the sum of the positive terms.
Now we will subtract the sum of the negative terms from the sum of the positive terms:
\[ 637 - 453 = 184 \]

### Final Answer:
The value of the expression \(3^{2} + 7^{2} + 11^{2} + 13^{2} + 17^{2} - 1^{2} - 5^{2} - 9^{2} - 11^{2} - 15^{2}\) is \(184\).

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