Can we subtract unlike terms?

The basic concept of algebra taught us how to express an unknown value using letters such as x, y, z, etc. These letters are termed here as variables. This expression can be a combination of both variables and constants. Any value that is placed before and multiplied by a variable is termed a coefficient. An idea of expressing numbers using letters or alphabets without specifying their actual values is defined as an algebraic expression.

Algebraic Expression

An expression that is made up of variables and constants along with algebraic operations such as addition, subtraction, etc. is termed an algebraic expression. These Expressions are made up of terms. Algebraic expressions are the equations when the operations such as addition, subtraction, multiplication, division, etc. are operated upon any variable.

A combination of terms by the operations such as addition, subtraction, multiplication, division, etc is termed as an algebraic expression (or) a variable expression. Examples: 2x + 4y – 7, 3x – 10, etc.

The above expressions are represented with the help of unknown variables, constants, and coefficients. The combination of these three terms is termed as an expression. Unlike the algebraic equation, it has no sides or ‘equals to’ sign.

Types of Algebraic expression

There are three types of algebraic expressions based on the number of terms present in them. They are monomial algebraic expressions, binomial algebraic expressions, and polynomial algebraic expressions.

• Monomial Expression: An expression that has only one term is termed a Monomial expression. Examples of monomial expressions include 4x⁴, 2xy, 2x, 8y, etc.
• Binomial Expression: An algebraic expression which is having two terms and unlike are termed as a binomial expression. Examples of binomial include 4xy + 8, xyz + x², etc.
• Polynomial Expression: An expression that has more than one term with non-negative integral exponents of a variable is termed a polynomial expression. Examples of polynomial expression include ax + by + ca, x³ + 5x + 3, etc.

Some Other Types of Expression

Apart from monomial, binomial, and polynomial types of expressions, there are other types of expressions as well that are numeric expressions, variable expressions,

• Numeric Expression: An expression that consists of only numbers and operations, but never includes any variable is termed a numeric expression. Some of the examples of numeric expressions are 11 + 5, 14 ÷ 2, etc.
• Variable Expression: An expression that contains variables along with numbers and operations to define an expression is termed A variable expression. Some examples of a variable expression include 5x + y, 4ab + 33, etc.

Some Algebraic Formulae

(a + b)² = a² + 2ab + b²

(a – b)² = a² – 2ab + b²

(a + b)(a – b) = a² – b²

(x + a)(x + b) = x² + x(a + b) + ab

(a + b)³ = a³ + b³ + 3ab(a + b)

(a – b)³ = a³ – b³ – 3ab(a – b)

a³ – b³ = (a – b)(a² + ab + b²)

a³ + b³ = (a + b)(a² – ab + b²)

Can we subtract unlike terms?

Answer:

Like terms: Terms that are having same variable or terms having variables with the same exponent power for them are called Like terms. 

Example: 6x & 16x and 5xy² & 8xy²

Here, 6x and 16x are called Like Terms because they have the same coefficient of x .

Unlike terms: Terms that are having different variables or terms having variables with different exponent power for them are called Unlike terms. 

Example: 7z & 16x and 7x² & 7x³

Here, 7z and 16x are called Unlike Terms because they have different coefficients of z and x .

The terms with the same variable with different exponents or different variable with same exponents are called Unlike terms. Only like terms can be subtracted. Unlike terms cannot be subtracted

The difference of one or more like terms is a single like term whereas the two unlike terms cannot be subtracted together to get a single term.

Let’s take a look at this with an example,

If 2x²+3xy+4x+7 is an algebraic expression.

Then, 2x², 3xy, 4x, and 7 are the Terms

Coefficient of the term: 2 is the coefficient of x²

Constant term: 7

Variables: Here x, y are variables

Factors of a term: If 2xy is a term, then its factors are 2, x, and y.

Like and Unlike Terms: Example of like and unlike terms:

• Like terms: 4x and 3x
• Unlike terms: 2x and 4y

Sample Questions

Question 1: Subtract 27z & 16x.

Answer:

Here the terms present are 27z & 16x,

= 27z – 16x is a term but this cannot be subtracted because both have different variables and are unlike terms.

Question 2: Identify like terms and unlike terms from the following:

5zy²x, 3y²z, 7xy²z, 3xz²y², 4x²yz

Answer:

Like Terms: 5zy²x,7xy²z

Now Unlike terms = 3y²z, 3xz²y², 4x²yz 

and unlike terms cannot be subtracted 

Question 3: Subtract (2x² – 5xy + 7 + z³) & (3x² + 4xy – 6 + 2z³)

Solution:

There are, (2x² – 5xy + 7 + z³) & (3x² + 4xy – 6 + 2z³)

Add and subtract  like terms together,

= (2x² – 5xy + 7 + z³) – (3x² + 4xy – 6 + 2z³)

= 2x² – 5xy + 7 + z³ – 3x² – 4xy + 6 – 2z³

= 2x² – 3x² – 5xy – 4xy + z³ – 2z³ + 7 + 6

= -x² – 9xy – z³ + 13