Which of the following terms are like terms?
a. 12ac2 and ac2
b. 9x and 9y
c. ab2 and x2y
d. 8xy and 8xz
Like terms are terms that have the same variables raised to the same power.
Looking at the given terms:
a. 12ac2 and ac2
These terms have the same variables (a and c) raised to the same power (2). Therefore, a. 12ac2 and ac2 are like terms.
b. 9x and 9y
These terms have different variables (x and y), so b. 9x and 9y are not like terms.
c. ab2 and x2y
These terms have different variables with different powers (b2 and x2y), so c. ab2 and x2y are not like terms.
d. 8xy and 8xz
These terms have the same variables (x and y) raised to the first power, but the last variable (z) is different. Therefore, d. 8xy and 8xz are not like terms.
In summary, the like terms are:
a. 12ac2 and ac2
To determine which of the given terms are like terms, we need to understand what like terms are. Like terms are terms that have the same variables raised to the same powers.
Let's analyze each option:
a. 12ac2 and ac2: These terms are like terms since they both have the variables ac^2 (variable 'a' raised to the power of 1, variable 'c' raised to the power of 2).
b. 9x and 9y: These terms are not like terms since they have different variables (variable 'x' and variable 'y').
c. ab2 and x2y: These terms are not like terms since they have different variables (variable 'a' and variable 'x'), and the exponents are also different (variable 'b' raised to the power of 2, and variable 'y').
d. 8xy and 8xz: These terms are like terms since they have the variables xy and xz. Both terms have variable 'x' raised to the power of 1, and variables 'y' and 'z'.
Therefore, the like terms among the given options are:
a. 12ac2 and ac2
d. 8xy and 8xz
all the variables and their powers have to match.
so, what do you think?