Question 83531


Addition of Polynomials:


Example:

1. Add (14x + 5)  and  (10x + 5)


Here we have two binomials..

First write them in a row as follows....

14x + 5 + 10x + 5


Now combine the similar terms.......


(14x + 10x)  + (5 + 5)

While adding terms containing like variable...you should add the constant term first and write the common variable as follows....


==> (14 + 10 )x + 10


==> 24x + 10


2. Add (19x2 + 12x + 12) and  (7x2 + 10x + 13) 

Here we have two trinomials(having three terms)

First write them in a row as follows....



(19x^2 + 12x + 12) +(7x^2 + 10x + 13) 



Now combine the similar terms.......



19x^2 + 7x^2 + 12x + 10x + 12 + 13 

As I explained in the previous example, While adding terms containing like variable...you should add the constant term first and write the common variable as follows....


==> (19 + 7)x^2 + (12 + 10 )x + (12 + 13 )



==> 26x^2 + 22x + 25



Subtraction of polynomials.



1. (6x + 14) - (9x + 5) 


Here first remove the parenthesis.....while doing that ...since you have a minus sign just infornt of the second polynomial, you should change the sign of each term of the second polynomial as follows......



6x + 14 - 9x - 5 


Now collect the like terms.....



6x -9x + 14 -5


==> (6-9)x + 14 -5



==> -5x + 9



2.(19x^2 + 9x + 16) - (5x^2 + 12x + 7)



==> 19x^2 + 9x + 16 - 5x^2 - 12x - 7



==>  19x^2 - 5x^2  + 9x - 12x + 16 -7



==> (19 -5)x^2 + (9-12)x + 16 -7



==> 14x^2 - 3x + 9




Hope you found the explanation useful.



Regards.



Praseena.