SOLUTION: Good evening how are you? I am having problems trying to understand how to do these problems, can you please help me with the above problems from the book and this problem x^5y^3-

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Question 88739This question is from textbook Intermediate Algebra
: Good evening how are you? I am having problems trying to understand how to do these problems, can you please help me with the above problems from the book and this problem x^5y^3-9x^4y^2+20x^3y the question states just to factor completely. Thank you so much I really appreciate it.
This question is from textbook Intermediate Algebra

Answer by jim_thompson5910(35256) About Me  (Show Source):
You can put this solution on YOUR website!
x%5E5y%5E3-9x%5E4y%5E2%2B20x%5E3y

x%5E3y%28x%5E2y%5E2-9xy%2B20%29 Factor out the GCF x%5E3y

Now what 2 numbers multiply to 20 and add to -9? These 2 numbers are -4 and -5

So these 2 numbers are placed into the blank expression

%28xy%2Ba%29%28xy%2Bb%29 where a=-4 and b=-5

x%5E3y%28xy-4%29%28xy-5%29 Plug in a=-4 and b=-5

Notice how %28xy-4%29%28xy-5%29 foils back to x%5E2y%5E2-9xy%2B20 so our answer is verified

So x%5E5y%5E3-9x%5E4y%5E2%2B20x%5E3y factors to x%5E3y%28xy-4%29%28xy-5%29