What are like and unlike terms?

Algebraic Expressions are made up of different terms coming together. Terms along with mathematical operations form an Algebraic Expression. Algebraic expressions are formed by coming together variables, operators, coefficients, and constants as an equation. An algebraic expression is composed of the following parts:

Parts of an algebraic expression

In an algebraic expression, there are different components, like terms, variables, constants, and coefficients. Let’s take a look at the definitions of these components,

• Terms: Terms are basically components such as variables with coefficients or simply constants that lead to the formation of an algebraic expression.
• Variables: Variables denote Changing values. Variables can take up any value and store that value.
• Constants: Constants are fixed numeric values. The value of constants do not change.
• Coefficients:  Coefficients are constant values that are directly attached to variables through multiplication or division operators.

Operators

• Operators are mathematical symbols such as +, -, ×, ÷.
• Operators bind different variables, coefficients, and constants together.

Example of algebraic expression

An example of algebraic expression would be: 60xy + 5z + 30

Here,

Variable: In the above expression xy and z are constants because it’s value changes with time.

Constant: In the above expression 30 is the constant term because its value doesn’t change with time.

Coefficient: In the above expression, 60 and 5 are coefficients of the terms xy and z respectively.

Operators: In the above expression, ‘+’ is the operator used in the expression.

Types of algebraic expressions

Depending on the number of terms in an algebraic expression. Further, there are different categories of Algebraic expression:

• Monomial algebraic expression

These are the algebraic expression containing only one term 

Example – 4x, xyz, 5yx, 8s, etc.

• Binomial algebraic expression

These are the algebraic expression containing two terms 

Example – 4x + 3, xyz – 4x, 5yx + 6s, 8s + 4, etc.

3. Trinomial algebraic expression

These are the algebraic expression containing three terms

Ex –  4x + 3z+ 2 , xyz -4x -4, 5yx + 6s+ z, 8s +4 + 14st etc.

• Polynomial algebraic expression

These are the algebraic expression containing more than three terms

Example – 4x + 3z + 2 + t, xyz – 4x – 4 + y, 5yx + 6s + z + yz, 8s + 4 + 14st + x, etc.

What are like and unlike terms give one example each?

Answer:

• Like Terms

Terms with the same variable i.e terms having variables with the same exponent power for them are called Like terms. Example: 5x & 16x

Here, 5x and 16x are called Like Terms because they have the same coefficient x, assigned to them.

• Unlike Terms

Terms with different variables i.e terms having variables with different exponent power for them are called, Unlike terms. Example: 5z & 16x

Here, 5z and 16x are called Unlike Terms because they have different coefficients z and x, assigned to them.

Conceptual Questions

Question 1: Identity LIKE TERMS to 5zy from the following:

7x⁴, 4z, 15yz, 10z³xy, 7x²y, 4zy

Answer: 

15yz and 4zy

Question 2: Only LIKE TERMS can be added/subtracted. True or False

Answer: 

True

Question 3: Only LIKE TERMS can be multiplied/divided. True or False

Answer:

False

Question 4: Identity LIKE TERMS from the following:

6zy²x, 3xy²z, 3xz²y, 4x²yz

Answer:

Like Terms: 6zy²x, 3xy²z