How to Multiply like and unlike terms together?

Algebraic Expression is an expression composed of variables and constants as well as algebraic operations like addition, subtraction, and so on. These expressions are composed of terms. Algebraic expressions are equations that are formed when operations such as addition, subtraction, multiplication, division, and so on are performed on any variable.

An algebraic expression (or variable expression) is a combination of terms using operations like addition, subtraction, multiplication, division, and so on.

Example: 5x + 4y – 10, 5x – 15, etc..

Like terms are ones with the same variables and exponent power. These variables’ coefficients might differ. Algebraic-like terms are terms that are similar to one another. The terms where variables and their exponents are different from each other are termed, Unlike terms.

How to multiply like and unlike terms together?

Solution:

Like terms are ones with the same variables and exponent power.

In case of Multiplication:

1st case Like Terms: if we multiply two like terms then it can be possible because like terms can be multiplied together .

Example 1: Multiply 6x and 5x ?

Solution: 6x × 5x

= 30x²

Example 2: Multiply 2y² and 8y² ?

Solution: 2y² × 8y²

= 16y⁴

2nd case Unlike Terms: The terms where variables and their exponents are different from each other are termed as Unlike terms . In an expression, the coefficient and the variables are different .

Example 1: Multiply 6x and 5y ?

Solution: 6x × 5y

here 6x and 5y are unlike terms as they have different variables and different coefficient

= 30xy

Example 2: Multiply 2y² and 8z² ?

Solution: 2y² × 8z²

= 2×8 × y² × z²

= 16y²z²

3rd case Like and Unlike Terms:

Example 1: Multiply 2x × 4x × 5y ?

Solution : Given terms are : 2x , 4x , 5y

here 2x and 4x are like terms and 5y is unlike terms

now multiply together

= first multiply like terms together

= (2x × 4x )× 5y

= 8x × 5y

= 40xy

hence we can multiply like and unlike terms together .

Problems based on Multiplication of Like and Unlike terms

Problem 1: Multiply 2a and 4b?

Solution:

Given terms are 2a and 4b

both are unlike terms

= 2a × 4b

= 8ab

Problem 2: Multiply 2a, 4a, 5b?

Solution:

Given terms are 2a,4a and 5b

here 2a and 4a are like terms

= (2a × 4a) × 5b

now multiply unlike terms

= 8a² × 5b

= 40a²b

Problem 3: Multiply 3xy² and 6xyz?

Solution:

Given terms are: 3xy² and 6xyz

= 3xy² × 6xyz

= 18x²y³z

Problem 4: Multiply 3c²d and 8cde?

Solution:

Given terms are 3c²d and 8cde

= 3c2d × 8cde

= (3 × 8 )x (c² × c )× (d×d) × e

= 24c³d²e