Question 661744: prove that, if the difference of two numbers is 4, then the difference of their squares is a multiple of 8.
Answer by htmentor(1343)   (Show Source):
You can put this solution on YOUR website! prove that, if the difference of two numbers is 4, then the difference of their squares is a multiple of 8.
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Let the two numbers = m, n
Then m - n = 4 -> m = n + 4
m^2 - n^2 = (n+4)^2 - n^2 = n^2 + 8n + 16 - n^2 = 8n + 16 = 8(n + 2), which is a multiple of 8.
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