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