In this post we will learn the concept of unlike terms with examples.
To understand the chapter you should have basic understanding of constants, variables and terms.
All the concepts have been discussed in the site, request you to learn these chapters first.
What are Unlike Terms?
Two or more entities are said to be unlike terms when:
(a) they have different variables, or;
(b) have same variables with different power.
Note:
The coefficients of entity doesn’t have any influence in determining like or unlike terms.
Examples of unlike terms
(a) 3x and 5y
The given terms are unlike since both entities have different variable.
(b) \mathtt{7xy\ and\ 7x^{2} y}
First entity ⟹ 7xy
Power of x = 1
Power of y = 1
Second entity ⟹ \mathtt{7x^{2} y}
Power of x = 2
Power of y = 1
Though the entities have same variable x and y, they have different powers.
Hence they are unlike terms.
(c) \mathtt{xyz^{3} \ and\ 10xyz^{3}}
First entity ⟹ \mathtt{xyz^{3}}
Power of x = 1
Power of y = 1
Power of z = 3
Second entity ⟹ \mathtt{10xyz^{3}}
Power of x = 1
Power of y = 1
Power of z = 3
Both the entity have same variable & with same power.
Hence they are like terms.
(d) \mathtt{\frac{x}{y^{2}} \ and\ \frac{x^{2}}{y}}
Solution
First entity ⟹ \mathtt{\frac{x}{y^{2}}}
Rewriting the entity
\mathtt{\frac{x}{y^{2}} \ \Longrightarrow \ x\ y^{-2}}
Power of x = 1
Power of y = -2
Second entity ⟹ \mathtt{\frac{x^{2}}{y}}
Rewriting the entity
\mathtt{\frac{x^{2}}{y} \ \Longrightarrow \ x^{2} \ y{^{-1}}}
Power of x = 2
Power of y = -1
Both the entities have variable with different power.
Hence they are unlike terms.
(e) \mathtt{x^{4} y^{2} z\ and\ x^{4} y^{2} z^{-1}}
First entity ⟹ \mathtt{x^{4} y^{2} z}
Power of x = 4
Power of y = 2
Power of z = 1
Second entity ⟹ \mathtt{x^{4} y^{2} z^{-1}}
Power of x = 4
Power of y = 2
power of z = -1
Both the entities have same variable x, y and z. But the power of variable z is different in the given entities.
Hence both the entities are unlike terms.
Frequently asked question – Unlike Terms
(01) How is like and unlike terms different?
Like terms have variables with same power.
On the other hand, in unlike terms, both the entities have variable with different power.
(02) Can we add/subtract the unlike terms in algebraic equation?
No!!
Unlike terms cannot be added/subtracted.
This is only possible in the case of like terms.
Example 01
Add 2xy + 13xy
Solution
Both the above entities are like terms, so addition is easily possible.
⟹ 2xy + 13xy
⟹ 15xy
Example 02
Add 9x + 15xy
Solution
The above entities are unlike terms.
Hence addition is not possible