SOLUTION: I am needing help please. Completly factor the expression and show all work: 245x^3-420x^2y+180xy^2

Question 407821: I am needing help please.
Completly factor the expression and show all work:
245x^3-420x^2y+180xy^2
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 49 and 36 respectively.

Now multiply the first coefficient 49 and the last coefficient 36 to get 1764. Now what two numbers multiply to 1764 and add to the middle coefficient -84? Let's list all of the factors of 1764:

Factors of 1764:
1,2,3,4,6,7,9,12,14,18,21,28,36,42,49,63,84,98,126,147,196,252,294,441,588,882

-1,-2,-3,-4,-6,-7,-9,-12,-14,-18,-21,-28,-36,-42,-49,-63,-84,-98,-126,-147,-196,-252,-294,-441,-588,-882 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to 1764
1*1764
2*882
3*588
4*441
6*294
7*252
9*196
12*147
14*126
18*98
21*84
28*63
36*49
42*42
(-1)*(-1764)
(-2)*(-882)
(-3)*(-588)
(-4)*(-441)
(-6)*(-294)
(-7)*(-252)
(-9)*(-196)
(-12)*(-147)
(-14)*(-126)
(-18)*(-98)
(-21)*(-84)
(-28)*(-63)
(-36)*(-49)
(-42)*(-42)

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

Now which of these pairs add to -84? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -84

First Number	Second Number	Sum
1	1764	1+1764=1765
2	882	2+882=884
3	588	3+588=591
4	441	4+441=445
6	294	6+294=300
7	252	7+252=259
9	196	9+196=205
12	147	12+147=159
14	126	14+126=140
18	98	18+98=116
21	84	21+84=105
28	63	28+63=91
36	49	36+49=85
42	42	42+42=84
-1	-1764	-1+(-1764)=-1765
-2	-882	-2+(-882)=-884
-3	-588	-3+(-588)=-591
-4	-441	-4+(-441)=-445
-6	-294	-6+(-294)=-300
-7	-252	-7+(-252)=-259
-9	-196	-9+(-196)=-205
-12	-147	-12+(-147)=-159
-14	-126	-14+(-126)=-140
-18	-98	-18+(-98)=-116
-21	-84	-21+(-84)=-105
-28	-63	-28+(-63)=-91
-36	-49	-36+(-49)=-85
-42	-42	-42+(-42)=-84

From this list we can see that -42 and -42 add up to -84 and multiply to 1764

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 )

note: is equivalent to since the term occurs twice. So also factors to

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

So our expression goes from and factors further to

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

So factors to

If you need more help, email me at jim_thompson5910@hotmail.com

Also, please consider visiting my website: http://www.freewebs.com/jimthompson5910/home.html and making a donation. Thank you

Jim
RELATED QUESTIONS
I am needing help please. Completly factor the expression and show all work:... (answered by jim_thompson5910)

I am looking for help on my algebra problem. Completly factor the following... (answered by stanbon)

I am needing some help please. Factor out the GCF from the expression and show work. (answered by ankor@dixie-net.com)

I am needing help on this problem... Please Find the quotient and show all work.... (answered by stanbon)

I am needing help on this problem for my kids' homework. SHOW ALL WORK: Factor out... (answered by Alan3354)

I really am needing some help with this please. Solve and show all work.... (answered by MathLover1)

I am needing help on this problem... Please Find the product and show all work.... (answered by Alan3354)

Completely factor the expression 72x^2y+48xy^2+8y^3 show all work please. (answered by KMST)