Vertical Subtraction of Algebraic Expression –
Step.1) Write the subtrahend ( that is, the expression to be subtracted ) below the minuend ( that is, the expression from which to subtracted ) in such a way that the like terms are in the same column.
Step.2) Change the sign of each term of the subtrahend.
Step.3) Then add the expression.
Example.1) Subtract 12xy – 5y from 22xy + 8x
Ans.) 22 xy + 8x
12 xy - 5y
- + ( changing the sign of the each term )
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10 xy + 8x + 5y
( where, 22 – 12 = 10, 8 – 0 = 8, and 0 + 5 = 5 ) (Ans.)
Example.2) Subtract 8a²- 8ab + 10 from 15a² + 5b⁴ - 12ab + 22
Ans.) 15a²+ 5b⁴ - 12ab + 22
8a² - 8ab + 10
- + - ( changing the sign of the each term )
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7a² + 5b⁴ - 4ab + 12
( where, 15 – 8 = 7, 5 – 0 = 5, - 12 + 8 = - 4, and 22 - 10 = 12 ) (Ans.)
Example.3) Subtract 5a² + 12ab – 10 from the sum of 12a² - 10ab + 4b²- 15 and 15a² + 5b⁴ - 12ab + 22
Ans.) First we have to add 12a² - 10ab + 4b² - 15 and 15a² + 5b⁴ - 12ab + 22
12a² - 10ab + 4b² - 15
+ 15a² - 12ab + 22+ 5b⁴
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27a² - 22ab + 4b² + 7 + 5b⁴
Now, we have to subtract 5a² + 12ab – 10 from 27a² - 22ab + 4b² + 7 + 5b⁴
27a² - 22ab + 4b² + 7 + 5b⁴
5a² + 12ab - 10
- - +
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22a² - 34ab + 4b² + 17 + 5b⁴ (Ans.)