Question 387234: Not understanding please help?
Completely factor the expression
27x2y + 180xy2 + 75y3
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website!
 Start with the given expression.
 Factor out the GCF  .
Now let's try to factor the inner expression 
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Looking at the expression , we can see that the first coefficient is  , the second coefficient is  , and the last coefficient is  .
Now multiply the first coefficient by the last coefficient to get  .
Now the question is: what two whole numbers multiply to  (the previous product) and add to the second coefficient ?
To find these two numbers, we need to list all of the factors of (the previous product).
Factors of :
1,3,5,9,15,25,45,75,225
-1,-3,-5,-9,-15,-25,-45,-75,-225
Note: list the negative of each factor. This will allow us to find all possible combinations.
These factors pair up and multiply to .
1*225 = 225
3*75 = 225
5*45 = 225
9*25 = 225
15*15 = 225
(-1)*(-225) = 225
(-3)*(-75) = 225
(-5)*(-45) = 225
(-9)*(-25) = 225
(-15)*(-15) = 225
Now let's add up each pair of factors to see if one pair adds to the middle coefficient :
| First Number | Second Number | Sum | | 1 | 225 | 1+225=226 | | 3 | 75 | 3+75=78 | | 5 | 45 | 5+45=50 | | 9 | 25 | 9+25=34 | | 15 | 15 | 15+15=30 | | -1 | -225 | -1+(-225)=-226 | | -3 | -75 | -3+(-75)=-78 | | -5 | -45 | -5+(-45)=-50 | | -9 | -25 | -9+(-25)=-34 | | -15 | -15 | -15+(-15)=-30 |
From the table, we can see that there are no pairs of numbers which add to . So cannot be factored.
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Answer:
So simply factors to
In other words,  .
If you need more help, email me at jim_thompson5910@hotmail.com
Also, feel free to check out my tutoring website
Jim
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