Algebraic Proof Question

Question

Using algebra,prove that, given any 3 consecutive even numbers, the difference between the square of the largest number and the square of the smallest number is always 8 times the middle number.

Answer 1

let suppose three consecutive numbers are: , X- 2, X, X+4

As per condition (X+2)² - (X -2) ² = X² + 4 + 4X - (X² +4 - 4X)

= X² + 4 + 4X - X² -4 + 4X

= 4X + 4X = 8X

PROVED