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What is the coeffiecient of x^3 in (x^2 + x + 1)^4?

 Jun 18, 2021

Best Answer 

 #1
avatar+2248 
+1

There are 2 combinations of x^2, x, and 1 that will have x^3. 

x^2, x, 1, 1 and x, x, x, 1

x^2, x, 1, 1 = 4*3*2/2 = 12 ways to organize

x, x, x, 1 = 4*3*2/3/2 = 4 ways to organize

4 + 12 = 16

 

=^._.^=

 Jun 18, 2021
 #1
avatar+2248 
+1
Best Answer

There are 2 combinations of x^2, x, and 1 that will have x^3. 

x^2, x, 1, 1 and x, x, x, 1

x^2, x, 1, 1 = 4*3*2/2 = 12 ways to organize

x, x, x, 1 = 4*3*2/3/2 = 4 ways to organize

4 + 12 = 16

 

=^._.^=

catmg Jun 18, 2021
 #2
avatar+121047 
+1

That's  an  interesting method, catmg.....I  haven't seen  that  before.......where did you  find this   (or learn it  ??? )

 

 

 

cool cool cool

CPhill  Jun 18, 2021
 #3
avatar+2248 
+1

You're choosing one term from each thing you're multiplying by. 

It's similar to the idea of the binomial theorum.

For example...

(x+1)(x+1) or (x+1)^2

If you were to fully expand it. 

x*x + 1*x + x*1 + 1*1, in each pair, you're choosing 1 term from each "x+1". 

There is only 1 way to get an x^2, choosing x for the first pair, and then choosing it again in the second pair. 

There are 2 ways to get an x, choosing x first pair then a 1 second pair, or 1 first pair and x second pair. 

I hope that made sense. :))

 

=^._.^=

catmg  Jun 18, 2021
 #4
avatar+121047 
+1

OK....THX  !!!!

 

 

cool cool cool

CPhill  Jun 18, 2021

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