is j+j+2k the same as 2jk

Answer 1

Typically not, as long as j and k are unlike terms

it is the same as

2(j + k)

Not

2jk

I hope you find this useful.

Answer 2

j + j + 2k = 2j + 2k

Answer 3

Hi Jay,

j + j + 2k is not necessarily the same as 2jk. 2jk is the same thing as 2 x j x k, while the original expression of j + j + 2k can only be simplified to 2j + 2k unless you know more information about the nature of the variables j and k.

Answer 4

I agree with Sze Hei S. I would like to point out that you can arrive at the same conclusion by exploring what it would take for j + j + 2k to be the same as 2jk and whittling the problem down algebraically. That is,

j + j + 2k = 2jk

2j + 2k = 2jk (combine like terms on the left-hand side)

j + k = jk (divide by the greatest common factor (GCF))

j = jk - k (subtract k from both sides to isolate the j on the left-hand side)

j = k(j - 1) (factor out the GCF on the right-hand side)

j/(j - 1) = k (divide both sides by (j - 1) to get j's to one side and k on the other)

At this point, you could stop and ask yourself, does it have to be true that k equals j/(j - 1)? You could substitute some numbers to make the equation work (e.g., j = 2, k = 2), but you could also substitute others that would make the equation break down (e.g., j = 2, k = 3). With such conflicting information, it cannot be true that j + j + 2k must be the same as 2jk. Creativity can provide a useful approach on a standardized test math section; sometimes it helps to look at the question in a different way.

Good luck with your studies.