What are like terms in Algebra?
Like terms in algebra are terms containing the same variables raised to the same exponent (or power). Like terms may have different coefficients.
Example 1
2 x , 3 x , (1/2) x , 0.1 x are all like terms since they contain the same (one) variable x to the same power 1.(Remember x = x^{1})
Example 2
2 x and 4 x^{2} are not like terms since they contain the same (one) variable x but not to the same power: the power of x in the term 2 x is equal to 1 and the power of x in the term 4 x^{2} is 2.
Example 3
 (1/2) x y^{2} and 8 x y^{2} are like terms since they contain the same variable x and y to the same power: the power of x is 1 in both terms and the power of y is 2 in both terms.
Example 4
5 x^{3} y^{2} , 11 x y^{2} are not like terms since they contain the same variable x and y BUT not to the same power: the power of x in the term 5 x^{3} y^{2} is 3 and the power of x in the term 11 x y^{2} is 1.
Multiple Choice Questions

Which of the lists below contains like terms only?

2x , 3x^{2} , x y , 1/x
  x , 3 x , 4
 x , x , 4x , 0.2 x , (1/4) x

x , 3 , 99 x , 9

Which of the terms below is a like term to  6 x y?
  6 x

 6 x y^{2}

 6 x y^{1}

 10 x y

Which of the lists below contains unlike (not like) terms?
 2x , 3x , x , 0.01 x

x , 5x^{2} , 99 x y , 9
 x , x , 4x , 0.2 x , (1/4) x

 2 , 7 , 4 , 89

Which of the lists below contains like terms only?

6x , 3x^{2} ,  10 x y , 1/x
  x , 3 x , 4
 x y , 3 x y , 0.002 x , (1/4) x y

x y , 3 x y , 0.002 x y , (1/4) x y

Which of the terms below is a like term to  x^{2} y?

 4 y x^{2}

 x y^{2}

 8 y x^{2}

 x y

Which of the terms below is a NOT a like term to 3 x y^{2}?

 4 y^{2} x

 (1/6) x y^{2}

 8 x y^{2}

0.00001 x y^{2}

Which of the lists below contains unlike (not like) terms?

2 y^{2} x^{2} , 3 x^{2} y^{2} , x^{2} y^{2} , 0.09 y^{2} x^{2}

x^{2} y^{2} , 7 x^{2} y, 99 x y , 11
  4 x , x , 4.5 x , 12 x , (1/8) x

 11 , 0.002 , 1/2 , 4.5

Which of the lists below contains like terms only?

3 x^{2} y^{3} , 3 y^{2} x^{3} ,  10 y^{2} x^{3} , 1/y^{2} x^{3}

 x , 3 x^{2} , 4 y^{2} x^{2}

x y , 3 x^{2} y^{2} , 0.002 x , (1/4) x y

 x^{3} y^{3} , 3 y^{3} x^{3} , 0.04 x^{3} y^{3} , 1.2 x^{3} y^{3}

Of the four terms below which is not a like term to the three others?

 y^{4} x

 (1/2) x y^{4}

 y^{4} x^{4}

 12 y^{4} x

Which of the terms below is a NOT a like term to 9?

 4.99 y^{0}
  (1/6)
  0.007

 9 x

