Question
The difference between the squares of two consecutive odd integers is always divisible by:
Answer: Option D
- Let the two consecutive odd integers be (2x + 1) and (2x + 3)
Then, (2x + 3)2 - (2x + 1)2 = (2x + 3 + 2x + 1) (2x + 3 - 2x - 1) = (4 x + 4) x 2
= 8 (x + 1), which is always divisible by 8
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- Let the two consecutive odd integers be (2x + 1) and (2x + 3)
Then, (2x + 3)2 - (2x + 1)2 = (2x + 3 + 2x + 1) (2x + 3 - 2x - 1) = (4 x + 4) x 2
= 8 (x + 1), which is always divisible by 8
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