Factoring Algebraic Expressions

Date: 6/15/96 at 0:52:47
From: Saul Miller
Subject: Factoring algebraic expressions

Is this the right place to ask for help on factoring?. If yes, 
please can you help me with these factoring problems?

Factor:

1) (xy+1)(x+1)(y+1)+xy

2) (1-y)^2 x^4-2x^2(1+y^2)+(1+y)^2

3) (b-c)(x-a)^2+(c-a)(x-b)^2+(a-b)(x-c)^2

Date: 6/17/96 at 11:54:8
From: Doctor Paul
Subject: Re: Factoring algebraic expressions

In number one, you've got a problem like this:
[A * B * C] + D

Note that [(A*B)*C]+D would yield the same result.

Let's begin by multiplying the 'A' and the 'B' terms;
that is, (xy+1)*(x+1)  

When given something in the form (G+H)(I+K), here's how to expand it:
G*I + G*K + H*I + H*K

When applied to the problem above, we have:

(xy*x)+(xy*1)+(1*x)+(1*1) = x^2y + xy + x + 1

So now we've got A*B. We must now multiply that term by 'C' 
(which is y+1)

Now we've got (y+1) * (x^2y + xy + x + 1).

Just as when we expanded above, we multiply each term in 
the first equation (y+1) by each term in the second equation 
(x^2y+xy+x+1) and then add them up.

(y*x^2y)+(y*xy)+(y*x)+(y*1)+(1*x^2y)+(1*xy)+(1*x)+(1*1)

Now simplify:

(y^2*x^2)+(xy^2)+(xy)+(y)+(x^2y)+(xy)+(x)+(1)

Note that we've got two xy's in there so let's add them up:

x^2y^2 + xy^2 + x^2y + 2xy + x + y + 1

Problems 2 and 3 use the same rules mentioned above.  Why don't you 
try them yourself?  If you still have trouble, write back and we'll 
help you again.

-Doctor Paul,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/