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.Com
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) (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.
---------------
1st: 2x
2nd: 2x+2
------
(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.
==================================
Cheers,
Stan H.
=======================
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
n & n+2 are the numbers
2*(n + n+2) = 2n+4
----------------
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.
RELATED QUESTIONS
The difference of squares of two consecutive even natural numbers is 60. Find the... (answered by stanbon,ikleyn,MathTherapy)
The difference between two numbers is 2, and the sum of their squares is 52. Find the... (answered by jorel555)
the difference between the squares of two consecutive numbers is 31. find the... (answered by richwmiller)
The sum of the squares of two consecutive even numbers is 6500. Find the... (answered by Alan3354)
The sum of the squares of 2 consecutive even positive umbers is 452. Find the... (answered by jim_thompson5910)
The sum of the squares of two numbers is 90. The difference between them is 6. Find the... (answered by mananth,benazir.sj@gmail.com)
The difference between the squares of two consecutive odd no. is 80.Find the... (answered by asuar010)
The sum of two numbers is 8 and the difference between their squares is 34. Find their... (answered by rakhileshnaidu,Alan3354)
the sum of the squares of two consecutive even numbers is 244.find the... (answered by vidhyak)