Combining Like Terms

In this lesson, we will look at how to add and subtract like terms. Algebra tiles are used to help see the concepts. Perimeter and word problem examples included.

 

Review

Like terms have the same variables and the same. To add like terms we just need to add the coefficients, which is usually the number part in front of the variable. After we have added the coefficients the variable will not change.
 

Try these problems:

 
     1.  Anders is planning to plant a garden in his back yard. He wants the length to be three times as long as the width. What is the perimeter of the garden?
 
     2.  $2x+2y+x^2-x+x^2$
 
     3.  $5xy+x^2y-2yx+3xy^2$
 
 

Answer:

1a. Draw a picture of the garden and label the sides. combining like terms
 b. To find the perimeter add all the sides.        $w + 3w + w + 3w$
  c. Combine like terms.        $1w + 3w + 1w + 3w =$ $8w$
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2a. $2x$ and $-x$ are like terms since they have the same variable $2x$ $+2y+x^2$$-x$ $+x^2$
 b. $x^2$ and $x^2$ are like terms since they have the same variable and exponents $x$ $+2y+$ $x^2+x^2$
 c. Solution: $x+2x^2$
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3a. $5xy$ and $2yx$ are like terms since they have the same variables and the order does not matter $5xy$ $+x^2y$$-2yx$ $+3xy^2$
 b. $x^2y$ and $xy^2$ are not like terms. $x^2y=xxy$ and $xy^2=xyy$
 c. Solution: $3xy +x^2y+3xy^2$