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Basic Algebra
Combining Like Terms: At a Glance

Introduction to Combining Like Terms:

Algebraic terms can, and often should, be combined and simplified. However, only terms that are "like", meaning that they have the exact same variables in each of them, can be added or subtracted. Furthermore, the variables have to have the same exponent to be "like"; xy2 and xy are not like terms, since y is squared in the first term.

Combining like terms is pretty simple, as long as you are careful with your negative and positive numbers. (For a quick review, check out adding integers and subtracting integers.) When adding and subtracting like terms, all you really need to do is combine the coefficients.

3x + -9x= -6x(picture)

Look Out: you can only combine terms with the exact same variables with the same exponents!

It can seem a little more complicated when dealing with subtraction. You must be extremely careful to keep the operations with the correct terms. In the example:

2y + 5x -8y (pictures)

there are two terms that can be combined (2y and 8y). However, it is "minus 8y" and we MUST be careful to keep the subtraction sign. 2y – 8y = -6y. This expression simplifies to:

-6y +5x(picture)

It is also worthy to note that the order of addition does not matter. This expression could also be written as 5x +-6y or 5x – 6y.

In each example below, we will draw shapes around the like terms

Combining Like Terms Practice:

Example 1

Simplify:

3xy + 3x^2y + -6xy +7xy^2


Example 2

Simplify:

(2x^2 + 3x) + (-6x - 5x^2)


Example 3

Simplify:

(4ab + 5b) - (2ab + 3a - b)


Exercise 1

Simplify: 3mn + -2n^2 + 4m - 8mn - 7m


Exercise 2

Simplify: (2x^2 + 5x - 1) + (5x^2 - 2x +9)


Exercise 3

Simplify: (2xy + 6x - 2y) - (-3xy + 4x - 7y)


Exercise 4

Simplify:  (7a +3b - 2)n- (4a - 7b - 5) -(a + b + 1)


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