Question

okay so this is for my homework and i have never really understood " LIKE TERMS"
so could any one help me

what is the like term of 5x, -7y, -x, y/2, 5x/7, x and y

Answer 1

In essence, like-terms have the same variables to the same powers. We can ignore the coefficients / the numbers multiplied onto the variables.
For example,
5x, -x, 5x/7, and x are all like-terms. This is because they all have the same variable x.
5* x, -1 * x, 5/7 * x, and 1 * x. Always has an x to the first power multiplied onto it.

When you are asked to "combine like terms", we can un-distribute that variable from like-terms:
5x - x + 5/7 x = (5 - 1 + 5/7) * x Notice you can return to the first statement just by multiplying through with x again.
It doesn't work, though, when you have two different terms:
5x - 7y Nothing will factor here. If we try to pull something out, we'll still have a messy expression.
(5 - 7y/x) * x

Answer 2

It is important also that we say they have to be the same variables to the same power, as well, just because we cannot add things like this either:
2x + x^2 =/= 3x or 3x^2.
2x and x^2 are not like-terms because one is a first-power x and the other is 2nd-power. By factoring:
x(2 + x) This also does not "combine" into one nice form like x + 2x = (1+2)x = 3x