Question 319069: I am trying to factor completely, I am not getting the concept.
My problem says factor completely: 24x^2y^3+16xy^4+48y^3, I do not know where to begin.
Found 2 solutions by CharlesG2, solver91311:
Answer by CharlesG2(834)   (Show Source):
You can put this solution on YOUR website! "I am trying to factor completely, I am not getting the concept.
My problem says factor completely: 24x^2y^3+16xy^4+48y^3, I do not know where to begin."
24x^2y^3 + 16xy^4 + 48y^3 (see what is common in the terms)
8 * 3 * x^2 * y^3 + 8 * 2 * x * y * y^3 + 8 * 6 * y^3
8y^3 is common to all the terms
if you take 8y^3 away from all terms you get:
3x^2 + 2xy + 6
8y^3(3x^2 + 2xy + 6)
Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
The first term,  which can be expressed as  , has three factors of 2, one factor of 3, two factors of  and three factors of  .
The second term,  which can be expressed as  , has four factors of 2, ZERO factors of 3, one factor of and four factors of .
The third term,  which can be expressed as  , has four factors of 2, one factors of 3, ZERO factors of and three factors of .
The fewest times that the factor 2 appears in any of the terms is 3 times.
The fewest times that the factor 3 appears in any of the terms is ZERO times.
The fewest times that the factor appears in any of the terms is ZERO times.
The fewest times that the factor appears in any of the terms is 3 times.
Hence, the largest factor that is in common with all three terms, i.e. the greatest common factor or GCF, is 
Hence:
)
John
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