## Thursday, 9 February 2012

### Multiplying Trinomials

Hello friends as I believe you have understood the previous topics in algebra, I am going to discuss about what Multiplying Trinomials is, what the examples of multiplying trinomials are and how to multiply trinomials. Firstly we will talk about how to multiply trinomials. For learning trinomial multiplication we need to know what is a trinomial so we will discuss first about trinomial then we will move to find out what is multiplication of trinomial. (To get help on cbse click here)
Trinomial is on the whole a part of polynomials. ‘Tri’ means three so trinomial can be seen as an expression that contains three terms. It has broad applications in quadratic functions. 2a+3b+7 is a trinomial because it contains three terms 2a, 3b and 7. So by this example we can create a general form i.e.-AX+BY+C.
When we multiply one trinomial with other trinomial it is called as multiplication of trinomials. Now we will discuss how to do multiplication operations between two trinomials with some examples -
Example 1 : What is the result of following multiplication -
(4x+5y+7) * (2x+3y-9) = ?
Solution : For solving these type of question we multiply each term with every term -
Step 1 : Firstly we multiply trinomial (4x+5y+7) with 2x -
(4x+5y+7) * 2x = 8x2+10xy+14x …....eq(1)
Step 2 : Now we multiply trinomial (4x+5y+7) with 3y -
(4x+5y+7) * 3y = 12xy+15y2+21y …....eq(2)
Step 3 : After this we multiply trinomial with 9 -
(4x+5y+7) * 9 = 36x+45y+63 ….....eq(3)
Step 3 : Now we perform operations which are giving in question -
so, we add eq(1) and eq(2) because here given that 2x+3y :
8x2+10xy+14x + 12xy+15y2+21y = 8x2+22xy+14x+21y+15y2 ….....eq(4)
Now, we subtract eq(3) from eq(4) :
8x2+22xy+14x+21y+15y2 – (36x+45y+63) = 8x2+22xy-22x-24y+15y2-63
So, the result of (4x+5y+7) * (2x+9) = 8x2+22xy-22x-24y+15y2-63
This is a Multiplying Trinomials example which shows how to multiply trinomials.
Now I think you have understood about the multiplication of polynomials. In the next topic we are going to discuss Solving Trinomial Multiplication and In the next session we will discuss about