SOLUTION: The difference between the squares of two consecutive even numbers is twise the sum of the numbers. For example: 8^2 - 6^2 = 28 2 x (8 + 6) = 28 Prove this resu

Algebra ->  Problems-with-consecutive-odd-even-integers -> SOLUTION: The difference between the squares of two consecutive even numbers is twise the sum of the numbers. For example: 8^2 - 6^2 = 28 2 x (8 + 6) = 28 Prove this resu      Log On


   

Question 416857: The difference between the squares of two consecutive even numbers is twise the sum of the numbers.
For example: 8^2 - 6^2 = 28
2 x (8 + 6) = 28
Prove this result algebraically.
thankyou :)
Found 2 solutions by stanbon, Alan3354:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
The difference between the squares of two
consecutive even numbers is twice the sum of the numbers.
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1st: 2x
2nd: 2x+2
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(2x)^2-(2x+2)^2 = 2(2x+2x+2)
---
4x^2-[4x^2+8x+4] = 8x+4
---
-8x-4 = 8x+4
Didn't work.
================
You have to take the square of the larger - the square of the smaller:
(2x+2)^2-(2x)^2 = 2(2x+2x+2)
---
4x^2+8x+4-4x^2 = 8x+4
8x+4 = 8x+4
That works.
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Cheers,
Stan H.
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Answer by Alan3354(69443) About Me  (Show Source):
You can put this solution on YOUR website!
n & n+2 are the numbers
%28n%2B2%29%5E2+-+n%5E2+=+n%5E2+%2B+2n+%2B+4+-+n%5E2+=+2n+%2B+4
2*(n + n+2) = 2n+4
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It's true for odd or even numbers, as shown above.
The difference between the squares is the difference between the numbers times the sum of the numbers.
Diff of squares = (Diff of numbers) * (sum of numbers)
There's no good reason to try to remember that, imo.