SOLUTION: Factor completely: x^7y^2 - 4x^5y^2 - 21x^3y^2 I am having a difficult time factoring this trinominal. Think I am getting confused by all the x's and y's. Could you please help

Click here to see ALL problems on Polynomials-and-rational-expressions

Question 73547This question is from textbook Intermediate Algebra
: Factor completely: x^7y^2 - 4x^5y^2 - 21x^3y^2
I am having a difficult time factoring this trinominal. Think I am getting confused by all the x's and y's. Could you please help me, so I can work these types of problems correctly? This question is from textbook Intermediate Algebra

Answer by bucky(2189) (Show Source):
You can put this solution on YOUR website!
Factor:
.

.
First look to see if there are any common factors in every term. Note that every term has
a in it. So pull that out and make it a multiplier of all the terms. You should
find that you have:
.

.
Look at what is left in the parentheses. All of the terms contain an so factor it
out and make it another multiplier of the expression remaining in the parentheses. When you
do the result is:
.

.
So far, so good. Now examine what's left in the parentheses. You may not recognize
it, but it can be factored like a quadratic. It may help you to see that if you let
then the expression in the parentheses would become:
.
and you may not be able to see that this factors to .
Then you can plug back in for A to get the two factors of
as being
.
So this is where we are at this point:
.

.
This may be good enough for the answer you are to provide, but there is one more mathematical
trick you can use on this. The term is the difference of two squares.
Therefore its factors are the sum and difference of the square roots of each term in
the parentheses. So factors to . This final
step completes what can be done by factoring. The result is:
.

.
This last step all depends on whether your teacher expects you to be working with radicals
in the answer.
.
Hope this helps.