CLASS-6
SUBTRACTION OF ALGEBRAIC EXPRESSION IN UNLIKE TERM

SUBTRACTION OF ALGEBRAIC EXPRESSION IN UNLIKE TERM -

Subtracting algebraic expressions with unlike terms involves subtracting the terms in one expression from the terms in another expression. Unlike terms are terms that have different variables or different variable exponents. When subtracting such expressions, you follow these steps:

1. Distribute the Subtraction (if needed):- If the expression you are subtracting is enclosed in parentheses, distribute the negative sign to all the terms within those parentheses. This ensures that you subtract each term individually.
2. Combine Like Terms Separately:- Organize the terms in both expressions into groups based on their similarity. Terms with the same variables or variable exponents should be in the same group. Separate these groups for each expression.
3. Subtract the Groups Separately:- For each group, add or subtract the terms separately. Combine the coefficients within each group, and retain the variable parts as they are.
4. Retain Unmatched Terms:- If there are any terms in one expression that do not have matches in the other expression, retain them as they are.
5. Write the Result:- Express the final result as a sum of the combined terms and any remaining terms.

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

Example.1) Subtracting Expressions with Unlike Terms

Given the expressions:

• 3x²+ 2y - 5
• 2x³- 4y + 1

Ans.)

Subtract the expressions separately by distributing the subtraction sign (this is already done in this case):

• (3x²+ 2y - 5) - (2x³- 4y + 1)

Now, organize the terms into groups based on similarity:

• Group 1:-  3x²and -2x³ (both involve the variable "x" but with different exponents).

• Group 2:-  2y and -4y (both involve the variable "y" with the same exponent).

• Group 3:-  -5 and 1 (both are constant terms).

Subtract the like terms within each group:

• Group 1:-   3x²- 2x³ = -2x³+ 3x²

• Group 2:-   2y - 4y = -2y

• Group 3:-  -5 - 1 = -6

Write the result as a sum of the combined terms and any remaining terms:

• (-2x³+ 3x²) - 2y - 6

So, the simplified expression after subtracting the expressions with unlike terms is -2x³+ 3x²- 2y - 6.

Example.2) Subtracting Expressions with Unlike Terms

Given the expressions:

• 3x²- 2y + 7
• 2x²+ 4y - 1

Ans.)

Distribute the subtraction sign and organize the terms:

• (3x²- 2y + 7) - (2x² + 4y - 1)

Combine like terms separately:

• (3x²- 2y + 7) - (2x²+ 4y - 1)
• (3x²- 2y) - (2x²+ 4y) + {7 - (-1)}

Now, subtract the like terms:

• (3x²- 2y) - (2x²+ 4y) + (8)

Combine the coefficients for like terms:

• (3x²- 2x²) - (2y + 4y) + (8)
• x²- 6y + 8

So, the simplified expression obtained by subtracting the unlike terms is x²- 6y + 8.

In this example, we distributed the subtraction sign, organized the terms, and then combined like terms separately before writing the final result.