Multiplication of Polynomials

Date: 3/20/96 at 16:2:26
From: Anonymous
Subject: multiplication of polynomials

I need to find the product for these two problems:

   1. 7(4m-3)(2m+1)  

   2. (2x-1)(3x exp.5 -2x exp.3+x exp.2-2x+3)

Date: 3/21/96 at 22:26:30
From: Doctor Steven
Subject: Re: multiplication of polynomials

For these two problems you need to use an algorithm called FOIL.
FOIL stands for first*first outer*outer inner*inner and last*last.

So we'll do the first problem first (imagine that)

  1. Find 7(4m - 3)(2m + 1).

     Step 1)  Multiply 7 and 4m - 3 to get:  28m - 21.
              Now the problem looks like (28m - 21)(2m + 1).

     Step 2)  Use FOIL.

              first * first = 28m * 2m = 56m^2 (56m exp.2 in your writing) 

              outer * outer = 28m * 1 = 28m

              inner * inner = -21 * 2m = -42m

              last * last = -21 * 1 = -21.

     Step 3)  Add the results from step 2 up to get:
                    56m^2 + 28m - 42m - 21.

     Step 4)  Simplify to get:
                    56m^2 - 14m - 7

     That's your answer.

  2. Find (2x - 1)(3x^5 - 2x^3 + x^2 - 2x + 3)

     This one's a little harder since you can't use FOIL on it (FOIL 
     only works on multiplications of things with two terms), but it 
     is still do-able so don't lose hope.

     Step 1) Multiply everything in second polynomial by 2x to get:

                     6x^6 - 4x^4 + 2x^3 - 4x^2 + 6x.

     Step 2) Multiply everything in second polynomial by -1 to get:

                     -3x^5 + 2x^3 - x^2 + 2x - 3.

     Step 3) Add these results together to get:

                     6x^6 - 3x^5 - 4x^4 + 4x^3 - 5x^2 + 8x - 3.

     That's your answer.

Hope this helps, on this problem and on future ones.

-Doctor Steven,  The Math Forum