Combining Like Terms Examples

Consider the expression 5x + 6x. Whoa...this expression looks mysteriously similar to the lemon dilemma. Or, "dilemmon." Can we combine like terms?

We can combine the like terms 5x and 6x to find 11x. We can do this step because of the distributive property:

5x + 6x = (5 + 6)x = 11x

Combine like terms in the expression 2 + 3x + 7x + 4xy.

There are two terms in this expression with the variable part x. Those terms are 3x and 7x. Combining those terms to get 10x, we have:

2 + 3x + 7x + 4xy = 2 + 10x + 4xy

Combine like terms in the expression 4 + 5y + y + 2x² + 3x².

We can combine the two terms with variable part y to get

4 + 6y + 2x² + 3x²,

and we can also combine the terms with variable part x² to get

4 + 6y + 5x².

Sometimes it is helpful to rearrange the terms such that like terms are next to each other. Just don't put them too close together unless they have both recently bathed.

Combine like terms:

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Use the distributive property to separate out the variables from the coefficients:

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Then add the fractions:

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