Hi



-4n^4 + 40n^3 - 100n^2 

-4n^2 (n^2 - 10n + 25)   |good work with this

-4n^2 (n-5)(n-5)    |to complete, the quadratic expression can be factored     

Note:SUM of the inner product(-5n) and the outer product(-5n) = -10n

Finaly, can be written

-4n^2 (n-5)^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 1 and 25 respectively.





Now multiply the first coefficient 1 and the last coefficient 25 to get 25. Now what two numbers multiply to 25 and add to the  middle coefficient -10? Let's list all of the factors of 25:









Factors of 25:



1,5





-1,-5 ...List the negative factors as well. This will allow us to find all possible combinations





These factors pair up and multiply to 25



1*25



5*5



(-1)*(-25)



(-5)*(-5)





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







Now which of these pairs add to -10? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -10






First Number
Second Number
Sum
1
25
1+25=26
5
5
5+5=10
-1
-25
-1+(-25)=-26
-5
-5
-5+(-5)=-10








From this list we can see that -5 and -5 add up to -10 and multiply to 25







Now looking at the expression , replace  with  (notice  combines back 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 

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