Question

find the product of three consecutive even intergers. if one of them is 2m

Answer 1

One of the consecutive number is 2m
Thus, the other two consecutive even numbers will be (2m-2) and (2m+2)

Thus,
Product of these numbers = (2m-2)(2m+2)2m
= 4m^2-4*(2m)
= 8m^3 - 8m
Thus the product of these three consecutive number is 8m^3 - 8m.

Or there's another method,

If one of the number is 2m
Then, the other two numbers will be (2m+2) and (2m+4)

Thus, the product of the numbers
= 2m(2m+2)(2m+4)
= 2m(4m^2 + 12m +8)
= 8m^3 + 24m + 16m

Answer 2

Answer:

Let 1st consecutive even integer is 2m

2nd consecutive even integer is 2m +2

3rd consecutive even unteger is 2m+4

product=2m(2m+2)(2m+4)

(4m^2 +4m) (2m+4)

8m^3 +8m^2+8m^2+16m

8m^3+16m^2+16m

8m(1+2m+2)

8m(3+2m)

hence this is the product of even consecutive integer