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Combining like terms review

A common technique for simplifying algebraic expressions. When combining like terms, such as 2x and 3x, we add their coefficients. For example, 2x + 3x = (2+3)x = 5x.

What is combining like terms?

We call terms "like terms" if they have the same variable part. For example, 4, x and 3, x are like terms, but 4, x and 3, w are not like terms.
The cool thing about like terms is that we can combine them into a single term by adding their coefficients. For example:
4x+3x=(4+3)x=7x\begin{aligned} &4x+3x\\\\ =&(4+3)x\\\\ =&7x \end{aligned}
Want to learn more about combining like terms? Check out this video.

More examples

An example with more than two terms:
2r+1+(4r)+7=2r4r+1+7=(24)r+1+7=2r+8\begin{aligned} &2\blueD{r} + 1 + (-4\blueD{r}) + 7\\\\ =& 2\blueD r - 4\blueD{r} + 1 + 7 \\\\ =& (2 - 4)\blueD{r} + 1 + 7 \\\\ =& -2\blueD{r} + 8 \end{aligned}
An example with more than one variable:
3x+2y+4x+7y=3x+4x+2yy+7=(3+4)x+(21)y+7=7x+y+7\begin{aligned} &3\blueD{x} + 2\goldD{y} + 4\blueD{x} + 7 -\goldD{y}\\\\ =&3\blueD{x} + 4\blueD{x} + 2\goldD{y} -\goldD{y}+7\\\\ =& (3+4)\blueD{x} + (2-1)\goldD{y} + 7 \\\\ =& 7\blueD{x} + \goldD y + 7 \end{aligned}

Check your understanding

Problem 1
Combine the like terms to make a simpler expression.
minus, 3, n, minus, 7, plus, left parenthesis, minus, 6, n, right parenthesis, plus, 1

Want more practice like this? Check out this exercise and this other exercise.

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