# CLASS-7COLUMN SUBTRACTION OF ALGEBRAIC EXPRESSION

COLUMN SUBTRACTION OF ALGEBRAIC EXPRESSION

To be noted –

To add algebraic expression, collect the like terms in groups and add the terms in each group, then we have to add the unlike terms.

The negative of an algebraic expression is obtained by changing the sign of the coefficient of each term of the expression.

To subtract an algebraic expression from another, add the negative of the first expression to the second.

Column Method –

Step.1) We have to write the subtrahend (the algebraic expression to be subtracted) below the minuend (the expression from which the subtrahend to be subtracted) such that the like terms are in the same column

Step.2) We would like to change the sign of each term of the subtrahend

Step.3) Add the two algebraic expression

Example-1)  Subtract  5x - 8y  from 15x – 7y

Ans.)                 15x – 7y

5x – 8y

-      +

---------------------

10x + y

Example-2)  Subtract  11x – 18y  from 15x – 25y

Ans.)                 15x – 25y

11x – 8y

-      +

------------------

4x – 17y

Example-3)  Subtract - 15x + 10y  from  - 10x – 22y

Ans.)               - 15x + 10y

- 10x – 22y

+     +

------------------

- 5x + 32y

Example.-4) The difference of two numbers is -10x⁴ + 8x²- 7x + 9, if the larger one is  22x⁴ - 16x² + 10x + 11 then find the smaller number.

Ans.)  As per the given instruction and formula –

Bigger number – Smaller number = Difference number

Let the smaller number is ‘A’, so as per condition –

=>  22x⁴ - 16x² + 10x + 11  - A =  -10x⁴ + 8x² - 7x + 9

=>   (22x⁴ - 16x² + 10x + 11) – (-10x⁴ + 8x² - 7x + 9)  =  A

=>   A   =   (22x⁴ - 16x² + 10x + 11) – (-10x⁴ + 8x² - 7x + 9)

=   22x⁴ - 16x² + 10x + 11 + 10x⁴ - 8x² + 7x – 9

=   32x⁴ - 24x² + 17x + 2

So the small number is 32x⁴ - 24x² + 17x + 2

OR

22x⁴ - 16x² + 10x + 11

- 10x⁴ +  8x² -  7x  + 9

+       -       +       -

--------------------------------

32x⁴ - 24x² + 17x + 2