SOLUTION: Not understanding please help? Completely factor the expression 27x2y + 180xy2 + 75y3

Algebra.Com
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


---------------------------------------------------------------


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 NumberSecond NumberSum
12251+225=226
3753+75=78
5455+45=50
9259+25=34
151515+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.


===============================================================



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

RELATED QUESTIONS

Completely factor the expression 27x2y + 90xy2 +... (answered by mathstutor494)
Need help please..... Completely factor the expression 343x3 – 98x2y +... (answered by stanbon)
Not understanding please explain? Factor out the greatest common factor from the... (answered by user_dude2008)
6. Completely factor the following expression: 36a^2 – 84ab + 49b^2 7. Completely... (answered by jim_thompson5910,richard1234)
Not understanding, can anyone help? Factor the expression a^2-6ab+96b^2 into a... (answered by jim_thompson5910)
Im lost, please help? Completely factor the expression 128x2 + 384xy + 72y2 (answered by Fombitz)
factor the expression completely m^3+11m^2+28m please help mee solve ti... (answered by stanbon,lwsshak3)
Hello everyone, I need help please? Completely factor the following expression: 49x2... (answered by Gogonati)
Factor the expression completely.. Please help!... (answered by Fombitz)