Like and Unlike Algebraic Terms

Before getting into like terms and unlike terms, you should be able to distinguish what an algebraic term is? You can understand this by using an example.

\(9x + 4y^{ 2 } = 5\) is an algebraic equation. It consists of 3 terms i.e. 9x, \(4y^{ 2 }\) and 5. The first two terms consists of variables and 5 is a constant.

9x + \(4y^{ 2 }\) is an algebraic expression. It has two terms 9x and \(4y^{ 2 }\).

Therefore algebraic terms are those individual elements in an equation or an expression separated by ‘+’ or ‘-’ signs.

Consider the expression: 9x + 6y

We cannot simplify this any further as ‘x’ and ‘y’ are unknown. Check out another example.

4×2 + 3x + 4y + 8x + \(10x^{ 2 }\)

If rearranged, this expression can be re-written as

\(10x^{ 2 }\) + \(4x^{ 2 }\) + 8x + 3x + 4y

which is equal to

\(14x^{ 2 }\) + 11x + 4y

Thus, it is seen that algebraic terms with same variables are added to each other.The addition of certain terms was possible only because the variables in both these cases are the same even if the numerical coefficients are different which can be added as normal numbers and the variable factor remains as it is. Now these terms which have the same variables are called like terms.

Thus, terms having identical variables raised to same exponent are like terms.

So, what are \(14x^{ 2 }\),, 11x and 4y called? These are called unlike terms since the variables or exponent raised to these variables are “unlike” or not same.

Further operations on unlike terms cannot be directly performed. Based on this, it is clear that an algebraic expression consists of terms which can be categorized into like terms and unlike terms.

Let’s consider another example 2xy + 4x² + 5xy +5y² +16x²

If you notice properly, the terms 2xy and 5xy, as well as 4x²and 16 x² have common factors. Only the numerical coefficients are different. Apart from that, all the variable factors are the same, so these terms can be added

2xy + 5xy = 7xy

4x² +16x² = 20 x²

Because these terms have the variable factors in common and an arithmetic operation can be performed on them they are called like terms. After adding the like terms, consider the expression again.

2xy + 4x² + 5xy +5y² +16x²=7xy + 20x² +5y²

If you observe the expression now, none of the terms have any common factors and no arithmetic operation can be performed on them further. These terms are called unlike terms.