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What is the value of 2^(2) - 1^(2) + 4^...

What is the value of `2^(2) - 1^(2) + 4^(2) - 3^(2) + 6^(2) - 5^(2)?`

A

3

B

16

C

17

D

21

Text Solution

AI Generated Solution

The correct Answer is:
To solve the expression \(2^2 - 1^2 + 4^2 - 3^2 + 6^2 - 5^2\), we can use the difference of squares formula, which states that \(a^2 - b^2 = (a + b)(a - b)\). Let's break down the expression step by step: 1. **Calculate \(2^2 - 1^2\)**: \[ 2^2 - 1^2 = (2 + 1)(2 - 1) = 3 \times 1 = 3 \] 2. **Calculate \(4^2 - 3^2\)**: \[ 4^2 - 3^2 = (4 + 3)(4 - 3) = 7 \times 1 = 7 \] 3. **Calculate \(6^2 - 5^2\)**: \[ 6^2 - 5^2 = (6 + 5)(6 - 5) = 11 \times 1 = 11 \] 4. **Combine all the results**: \[ 2^2 - 1^2 + 4^2 - 3^2 + 6^2 - 5^2 = 3 + 7 + 11 \] 5. **Calculate the final sum**: \[ 3 + 7 + 11 = 21 \] Thus, the value of the expression \(2^2 - 1^2 + 4^2 - 3^2 + 6^2 - 5^2\) is \(21\).
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