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ADDITION OF ALGEBRAIC EXPRESSION IN UNLIKE TERM

__ADDITION OF ALGEBRAIC EXPRESSION IN UNLIKE TERM -__

**When adding algebraic expressions with unlike terms, you cannot directly combine them like you would with like terms. Instead, you need to follow some key steps to add the expressions correctly. Here's how you can add algebraic expressions with unlike terms:**

__Identify and Group Like Terms:-__Begin by identifying and grouping like terms within each expression separately. Like terms are terms that have the same variables and exponents.__Place Each Expression in Parentheses:-__To avoid errors when adding unlike terms, place each expression within parentheses.

** For example, if you want to add the expressions (3x²+ 2x - 5) and (5y²- 7y + 1), you would write:- (3x²+ 2x - 5) + (5y²- 7y + 1)**

** 3. Perform the Addition:- To add the expressions, you can use parentheses to keep the terms separate and ensure that each term is added to the corresponding term in the other expression:-**

**(3x²+ 2x - 5) + (5y²- 7y + 1) = (3x²+ 2x) + (-5 + 5y²- 7y + 1)**

** 4. Combine Like Terms in Each Expression:- In this step, combine like terms within each expression separately.In the first expression, you have the quadratic term "3x²" and the linear term "2x." There are no constant terms in this expression, so leave it as it is. In the second expression, you have the quadratic term "5y²," the linear term "-7y," and the constant term "1."**

** 5. Write the Sum:- Combine the simplified terms from each expression to write the sum of the two algebraic expressions.The sum of the first expression is "3x²+ 2x."The sum of the second expression is "5y²- 7y + 1."**

**So, when adding the algebraic expressions (3x²+ 2x - 5) and (5y²- 7y + 1), you get the sum:**

** (3x²+ 2x) + (5y²- 7y + 1)**

**= 3x²+ 2x + 5y²- 7y + 1**

**The result is an algebraic expression with unlike terms, and you have added the two expressions correctly.**

**Here's an example of adding algebraic expressions with unlike terms:**

**Example.1) Adding Expressions with Unlike Terms**

**Given the expressions:**

**3x²+ 2y - 5****2x³- 4y + 1**

**Ans.) **

**Identify and group similar terms:**

__Group 1:__3x²and 2x³ (both are terms with the variable "x").__Group 2:__2y and -4y (both are terms with the variable "y").__Group 3:__-5 and 1 (both are constant terms).

**Now, add or subtract the groups separately:**

__Group 1:__3x²+ 2x³= 3x²+ 2x³ (you cannot combine these terms further).__Group 2:__2y - 4y = -2y.__Group 3:__-5 + 1 = -4.

**Write the result as a sum of the combined groups:**

**(3x²+ 2x³) + (-2y) + (-4)**

**So, the simplified expression with unlike terms is 3x²+ 2x³- 2y - 4.**

**Example.2) Given the expressions:**

**3x²- 2y + 7****4x²+ 5y - 3**

**Ans.) **

**Group the terms with similar characteristics:**

__Group 1__ (Terms with x²):

**3x²****4x²**

__Group 2__ (Terms with y):

**-2y****5y**

__Group 3__ (Constant Terms):

**7****-3**

**Now, add or subtract within each group:**

__Group 1:__ (3x²+ 4x²) = 7x²

__Group 2:__ (-2y + 5y) = 3y

__Group 3:__ (7 - 3) = 4

**Combine the results from each group:**

**7x²+ 3y + 4**

**So, the simplified expression for the addition of the given expressions with unlike terms is 7x²+ 3y + 4.**

**Remember to group terms based on their characteristics, perform addition or subtraction within each group, and combine constants to simplify algebraic expressions with unlike terms.**

**When adding algebraic expressions with unlike terms, the goal is to group and simplify as much as possible, but some terms may remain separate if they cannot be combined due to differences in variables or variable exponents.**