Addition of Algebraic Expression –
It must be known by you that, to add two or more algebraic expressions, group the like terms of the expressions and add each group of like terms separately. This method is known as the horizontal method of addition.
Example.1) Add 4x + 3y – 5z, 12x – 8y + 5z, and - 4x + 8y + 6z
Answer) The sum = (4x + 3y – 5z) + (12x – 8y + 5z) + ( - 4x + 8y + 6z)
= ( 4x + 12x – 4x ) + ( 3y – 8y + 8y ) + ( - 5z + 5z + 6z )
[ Grouping the like term ]
= ( 4 + 12 – 4 ) x + ( 3 – 8 + 8 ) y + ( - 5 + 5 + 6 ) z
[ Adding the like term ]
= 12 x + 3 y + 6 z (Ans.)
Alternative method –
We have to write the expressions one below the other such that the like terms are in the same column. Then add each column of like terms, this is known as the column method of addition.
4x + 3y – 5z
12x – 8y + 5z
- 4x + 8y + 6z
-------------------
12x + 3y + 6z (Ans.)
Example.2) Add 4x - 23y – 5z + 8, 2x + 8y - 15z, and 3x - 5y + 10z + 6
Answer) The sum = ( 4x - 23y – 5z + 8 ) + ( 2x + 8y - 15z ) + ( 3x - 5y + 10z + 6 )
= ( 4x - 23y – 5z + 8 ) + ( 2x + 8y - 15z ) + ( 3x - 5y + 10z + 6 )
[Grouping the like term]
= ( 4 + 2 + 3 ) x + ( - 23 + 8 - 5 ) y + ( - 5 - 15 + 10 ) z + ( 8 + 6 ) [Adding the like term]
= 9 x - 20 y - 10 z + 14
Alternative method –
We have to write the expressions one below the other such that the like terms are in the same column. Then add each column of like terms, this is known as the column method of addition.
4x - 23y – 5z + 8
2x + 8y - 15z
3x - 5y + 10z + 6
-----------------------------
9 x - 20 y -10 z + 14 (Ans.)