# Combining like terms

Combining like terms refers to the process of simplifying equations and expressions by adding or subtracting variables and their coefficients. Terms are said to be "like" if they have the same variable and exponent.

Example

Steve has a bag of potatoes and a bag of tomatoes. They are both different types of vegetables, and if treated as an equation, could not be combined.

1 tomato + 1 potato = 1 tomato + 1 potato

We cannot combine the vegetables in such a way that we would have 2 of some combined form of potatoes and tomatoes:

1 tomato + 1 potato = 2 ?

We could say that there are 2 vegetables, but for the purposes of this example, we simply want to demonstrate that the two cannot be directly combined.

Different variables and exponents are like different vegetables - they can't really be combined as you would combine numbers in an addition problem.

2x^{2} + 4x - 3y^{3} + 6x - 6y^{3}

4x and 6x have the same variable (x) and exponent (1) so you can combine them by adding their coefficients.

-3y^{3} and -6y^{3} have the same variable (y) and exponent (3), so you can combine them by subtracting their coefficients (because the coefficient is negative).

2x^{2} + (4 + 6)x + (-3 - 6)y^{3} = 2x^{2} + 10x - 9y^{3}

You cannot combine 4x and 2x^{2} because they have different exponents (1 and 2 respectively), just as you cannot combine 4x and -3y^{3} because they have different variables (x and y).