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 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.
===============================================================
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)