Multiplication Involving Trinomials
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Multiplying a Binomial and a Trinomial

 

Put the "distributive method" of multiplication to work.  Multiply each term from the binomial times each term of the trinomial.  You can do this by using either a horizontal method or a vertical method.
Note:  FOIL will not work in this problem.
 

Horizontal Method:

(x + 3)(x + 2x + 4)

 = x + 2x + 4x + 3x + 6x + 12
 = x + 2x + 3x + 4x + 6x + 12  Group like terms.
 = x + 5x + 10x + 12     Combine like terms.

 

Vertical Method:

x + 2x + 4

x + 3

Chocbrn.jpg (2624 bytes)

x + 2x + 4x

3x + 6x + 12

  Line up like terms.
Chocbrn.jpg (2624 bytes)

x + 5x + 10x + 12

  Add like terms.
 

 

 
 
 
Cubing a Binomial

 

Expand:   (x + 3)

If you take your time, this problem is really very simple.    All you need to do is multiply twice.  Multiply (x + 3) times (x + 3), and then  multiply that answer by (x + 3).  Simple!

(x + 3)

 = (x + 3)(x + 3)(x + 3)
 = (x + 3x + 3x + 9)(x + 3)     the first multiplication is done
 = (x + 3) (x + 6x + 9)       combine like terms and switch order
 = x + 6x + 9x + 3x + 18x + 27   multiply again
 = x + 9x + 27x + 27    combine like terms

The "distributive method" of multiplication was used in this problem.
Note:  FOIL will not work for the second multiplication in this problem.