Nature of p₁² − p₂² When p₁ and p₂ Are Odd Prime Numbers

Video Explanation

Watch the video below for a clear explanation:

Solution

Question: If p₁ and p₂ are two odd prime numbers such that p₁ > p₂, then p₁² − p₂² is:

(a) an even number    (b) an odd number    (c) an odd prime number    (d) a prime number

Step 1: Use Identity

p₁² − p₂² = (p₁ − p₂)(p₁ + p₂)

Step 2: Nature of the Factors

Since p₁ and p₂ are odd primes:

p₁ − p₂ = odd − odd = even
p₁ + p₂ = odd + odd = even

Step 3: Product of Two Even Numbers

Even × Even = Even

∴ p₁² − p₂² is an even number.

Final Answer

✔ p₁² − p₂² is an even number.

✔ Correct option: (a) an even number

Conclusion

Thus, the difference of the squares of two odd prime numbers is always an even number.