CLASS-6
SUBTRACTION OF ALGEBRAIC EXPRESSION IN LIKE TERM

SUBTRACTION OF ALGEBRAIC EXPRESSION IN LIKE TERM -

Subtracting algebraic expressions with like terms involves combining terms that have the same variables raised to the same exponents but with opposite signs. When subtracting such expressions, you follow these steps:

  1. Identify Like Terms:- First, identify the terms in the expressions that have the same variables with the same exponents. These terms are called "like terms." Like terms can be subtracted from each other.
  2. Combine the Coefficients:- Subtract the coefficients of the like terms. If the terms have opposite signs (one positive and one negative), you subtract the absolute values of the coefficients and assign the sign of the term with the larger absolute value.
  3. Retain the Variable Part:- Keep the variable part (with its exponent) the same. The variable part represents the common variable(s) shared by the like terms.
  4. Combine Constants:- If there are constant terms in the expressions, subtract them as well.
  5. Write the Result:- Write the simplified expression after subtracting the like terms.


Here are some examples of subtracting algebraic expressions with like terms:-

Example 1: Subtracting Like Terms

Given the expressions:

  • 5x²+ 3x - 7
  • 2x²- 4x + 1

Ans.) 

Identify and subtract the like terms:

  • (5x²- 2x²) + (3x + 4x) - (7 - 1)

Now, subtract the like terms:

  • 3x²+ 7x - 6

So, the simplified expression after subtracting the like terms is 3x²+ 7x - 6.



Example.2) Subtracting Like Terms with Negative Coefficients

Given the expressions:

  • 4y³- 2y² + 7y - 1
  • 2y³+ 3y²- 5y + 1

Ans.)

Identify and subtract the like terms:

  • (4y³- 2y³) - (2y²- 3y²) + (7y + 5y) - (1 - 1)

  =  2y³- (-y²) + 12y - (0)

Now, subtract the like terms:

  • 2y³+ y²+ 12y

So, the simplified expression after subtracting the like terms is 2y³+ y² + 12y.

When subtracting algebraic expressions with like terms, remember to combine the coefficients while retaining the variable parts. The result is a simplified expression with the combined like terms.

The difference between two like terms is a like term with a numerical coefficient equal to the difference between the numerical coefficient so f the two like terms We want to subtract

Solution:-

Ex.1) 5p from12p

=> 12p – 5p = 12*p – 5*p

=> (12 - 5)*p

=>  7*p

=>  7p

So, 12p – 5p = 7p       (Ans.) 



Ex.2) 9pq from 15pq Solution:

15pq – 9pq

= 6pq        (Ans.)



Ex.3) Subtract -7x from 5x

Solution:

=> 5x – (-7x)

=> 5x + 7x

=> 12x            (Ans.)