SOLUTION: What are the coefficients for the expansion (x+1)^6 One of the following is the correct answer. Which one? A) 1,6,15,20,15,6,1 B) 1,7,21,7,21,1 C) 1,5,10,5,1 D) 1,4,

Algebra ->  Polynomials-and-rational-expressions -> SOLUTION: What are the coefficients for the expansion (x+1)^6 One of the following is the correct answer. Which one? A) 1,6,15,20,15,6,1 B) 1,7,21,7,21,1 C) 1,5,10,5,1 D) 1,4,      Log On


   

Question 1198585: What are the coefficients for the expansion (x+1)^6
One of the following is the correct answer. Which one?
A) 1,6,15,20,15,6,1
B) 1,7,21,7,21,1
C) 1,5,10,5,1
D) 1,4,6,4,1
E) 1,6,9,12,9,6,1
Found 2 solutions by MathLover1, MathTherapy:
Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!

%28x%2B1%29%5E6

The binomial coefficients are represented as nC0, nC1,+nC2.....nC%28n-1%29
C%286%2C+1-1%29=C%286%2C+0%29=1
C%286%2C+2-1%29=C%286%2C+1%29=6
C%286%2C+3-1%29=C%286%2C+2%29=15
C%286%2C+4-1%29=C%286%2C+3%29=20
C%286%2C+5-1%29=C%286%2C+4%29=15
C%286%2C+6-1%29=C%286%2C+5%29=6
C%286%2C+7-1%29=C%286%2C+6%29=1

check:
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the coefficients are: 1,6,15,20,15,6,1

answer: A

Answer by MathTherapy(10555) About Me  (Show Source):
You can put this solution on YOUR website!

What are the coefficients for the expansion (x+1)^6
One of the following is the correct answer. Which one?
A) 1,6,15,20,15,6,1
B) 1,7,21,7,21,1
C) 1,5,10,5,1
D) 1,4,6,4,1
E) 1,6,9,12,9,6,1
You don't need to expand the BINOMIAL to find the coefficients, as Pascal's Triangle tells one that the 6th power yields coefficients: 

1, 6, 15, 20, 15, 6, 1.

You can see that the coefficents REPEAT, in reverse order after the MEDIAN coefficient. That's how ALL coefficents of a BINOMIAL 

EXPANSION behave. Look up Pascal's Triangle.

Never follow what that woman does! She is rarely right, and never wants to deviate from PLAGIARIZING, and learn the correct way

to do mathematics. I wouldn't put it past her to expand the binomial if it were to the 52nd power: (x + 1)52.