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Concept

# Combining Like Terms

When simplifying algebraic expressions, it is only possible to combine (add or subtract) like terms. $\begin{gathered} 7y+2x-3y-2+x+5 \end{gathered}$ This example expression contains three sets of like terms: $x\text{-terms},$ $y\text{-terms},$ and $\text{constants}.$

To simplify the expression, the terms should first be rearranged such that like terms are grouped together. Then, the like terms can be combined by adding or subtracting the constants as well as adding or subtracting the coefficients of the variables. \begin{aligned} \colorbox{#99ffbb}{+7y-3y} &\quad + & \colorbox{#b3e6ff}{+2x+x} &\quad + & \colorbox{#ffb3b3}{\text{-}2+5} \\ {\color{#009600}{4y}} \quad\ &\quad + & {\color{#0000FF}{3x}} \quad\ &\quad + & {\color{#FF0000}{3}}\quad \end{aligned} This is the simplest form of the expression.

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