TopThere may be two types of terms in an expression, these are like terms and unlike terms. Like terms can be defined as those terms which are comprised of same variables and exponents. Coefficients of like terms may be different and it is not necessary that they match with each other. Unlike terms are those terms in an expression which do not have same variables that is unlike terms are comprised of different variables and exponents. There is no importance of order of variables unless there is an exponent. We can also determine how to distribute and combine like terms? For instance, 12 a b c 2 and − 7 a b c 2 are like terms because same variables and exponents can be found in given expressions and 3a b c and 2 x y z are unlike terms since they have different variables. We know that coefficients do not have an effect on likeness hence all constant terms can be referred to like terms.
Let’s take an example to understand how to distribute and combine like terms?
10 (3 y + 6 x) = 6 (4 y – 3 x),
To solve above expression, we have to be familiar with both distributive and combining property. In distribution property, number 10 and 6 will be multiplied first with values inside the parenthesis. Thus above expression will be:
30 y + 60 x = 24 y – 18 x (using the distributive property),
Rearranging the above equation,
30 y + 60 x – 24 y + 18 x = 0,
Here two like terms exist which are 30y, – 24y and 60x, 18x,
Simple addition and subtraction operation will be performed that is
30 y – 24 y + 60 x + 18 x = 0,
6 y + 78 x = 0 (on simplifying).