can someone help me with this?

Question

Factor the polynomial completely.

 

yx−ya+xb−ab

Answer 1

Hi Candice,

 

    
Factor the polynomial completely.

yx−ya+xb−ab

 

This polynomial can be factored by a process called Grouping.

 

Start by putting parentheses around the 1st two terms and the last two terms:

 

(yx−ya)+(xb−ab)

 

I generally start with the second parentheses.  I ask what can be factored out of the binomial?  Looking at the two terms there is a common "b", so that can be factored out:

 

(yx−ya)+b(x−a)

 

Now, ask what can be factored out from the binomial in the 1st parentheses.  Looks like a "y"

 

y(x−a)+b(x−a)

 

The first factor is the binomial in the parentheses:  (x-a)

THe second factor is what is outside of both parentheses:   (y+b)

 

So, the factors of yx−ya+xb−ab  are:    (x-a)(y+b)

 

Hope that this helps you understand the process.

 

 

Answer 2

Review:

Remember FOIL (First-Outside-Inside-Last) and expand:

   (x + c)(y + d)        [note: use c,d because problem used a,b]

     xy + xd + cy + cd

 

Actually, FOIL is the result of using the Distributive Principle three times:

    (x + c)(y + d)

     (x)(y + d) + c(y + d)      [first use]

     xy + xd   + c(y + d)      [second use]

     xy + xd + cy + cd         [third use]

      F      O      I     L

 

Problem:  Now, we want to go in reverse.  Start with:

     xy + xd + cy + cd

     x(y + d) + cy + cd       [group the first two terms]

     x(y + d) + c(y + d)     [group the second two terms]

     (x + c)(y + d)             [the term (y+d) must be the same]

 

Key point:  You may need to rearrange the terms being added before grouping them.

 

Problem:  Factor the polynomial completely.   yx - ya + xb - ab

                          [rewrite]                                      yx - ya + bx - ba

                       [same process]                                   F   O    I     L

 

         (y + b)(x - a)