SOLUTION: I need to understand how to do this problem by factoring completely. I believe my first step is finding the common factors. Can someone show me step by step? 27y^5

SOLUTION: I need to understand how to do this problem by factoring completely. I believe my first step is finding the common factors. Can someone show me step by step? 27y^5 - 63y^4 + 30y

Question 221874: I need to understand how to do this problem by factoring completely. I believe my first step is finding the common factors. Can someone show me step by step?
27y^5 - 63y^4 + 30y^3
and
125-8u^3
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
# 1

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 9 and 10 respectively.

Now multiply the first coefficient 9 and the last coefficient 10 to get 90. Now what two numbers multiply to 90 and add to the middle coefficient -21? Let's list all of the factors of 90:

Factors of 90:
1,2,3,5,6,9,10,15,18,30,45,90

-1,-2,-3,-5,-6,-9,-10,-15,-18,-30,-45,-90 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 90
1*90
2*45
3*30
5*18
6*15
9*10
(-1)*(-90)
(-2)*(-45)
(-3)*(-30)
(-5)*(-18)
(-6)*(-15)
(-9)*(-10)

note: remember two negative numbers multiplied together make a positive number

Now which of these pairs add to -21? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -21

First Number	Second Number	Sum
1	90	1+90=91
2	45	2+45=47
3	30	3+30=33
5	18	5+18=23
6	15	6+15=21
9	10	9+10=19
-1	-90	-1+(-90)=-91
-2	-45	-2+(-45)=-47
-3	-30	-3+(-30)=-33
-5	-18	-5+(-18)=-23
-6	-15	-6+(-15)=-21
-9	-10	-9+(-10)=-19

From this list we can see that -6 and -15 add up to -21 and multiply to 90

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

In other words,

# 2

Start with the given expression.

Rewrite as . Rewrite as .

Now factor by using the difference of cubes formula. Remember the difference of cubes formula is

Multiply

-----------------------------------
Answer:
So factors to .

In other words,

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