SOLUTION: Factor completely. x^3y + 4x^2y^2

SOLUTION: Factor completely. x^3y + 4x^2y^2 - 21xy^3

Question 201040: Factor completely.
x^3y + 4x^2y^2 - 21xy^3
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 focus on the inner expression

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

Looking at we can see that the first term is and the last term is where the coefficients are 1 and -21 respectively.

Now multiply the first coefficient 1 and the last coefficient -21 to get -21. Now what two numbers multiply to -21 and add to the middle coefficient 4? Let's list all of the factors of -21:

Factors of -21:
1,3,7,21

-1,-3,-7,-21 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -21
(1)*(-21)
(3)*(-7)
(-1)*(21)
(-3)*(7)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to 4? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to 4

First Number	Second Number	Sum
1	-21	1+(-21)=-20
3	-7	3+(-7)=-4
-1	21	-1+21=20
-3	7	-3+7=4

From this list we can see that -3 and 7 add up to 4 and multiply to -21

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

So this also means that factors to (since is equivalent to )

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

So our expression goes from and factors further to

------------------
Answer:

So completely factors to

RELATED QUESTIONS
21xy+14x^3y^2 (answered by checkley77)

3x^3y+18x^2y-21xy (answered by ReadingBoosters)

Factor Completely... (answered by Earlsdon)

Completely factor the expression 147x^2y + 42xy^2 + 3y^3 (answered by scott8148,Earlsdon)

factor the polynomial completely.... (answered by Earlsdon)

Factor each polynomial completely x^3y+2x^2y^2+xy^3 (answered by stanbon)

Factor completely. 4x^2 + 3xy + 4x +... (answered by stanbon)

Factor completely 2x^3 + 4x^2y +... (answered by mananth)

facotr completely... (answered by oberobic)