Question

prove that the multiple of 4 consecutive numbers is always
$x {}^{2} - 1$

Answer 1

Answer:

As we know, every even number is a multiple of two. So, any even number N can be represented as 2×n (where n is another number, equal to N/2).

Let's assume two even numbers, X= 2x and Y=2y.

Multiplying X and Y,

X×Y=2x × 2y (from the above assumption)

= 4xy

=4d (where d=xy)

Hence proved that the product of any two even numbers is a multiple of 4 (or) divisible by 4

Answer 2

Let no be x-2,x-1,x,x+1

Product = (x-1)(x+1)(x-2)x

=(x^2-1)x(x-2)

Hence this is of form k (x^2-1)

k is an integer hence this proves that it is a multiple