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nirvana33 [79]
2 years ago
7

What are the coefficients for the binomial expansion of (a + b)^3?

Mathematics
2 answers:
lilavasa [31]2 years ago
7 0
The coefficients are given by \dbinom 3k=\dfrac{3!}{k!(3-k)!} where k\in\{0,1,2,3\}. These are, in order, \{1,3,3,1\}.

So the expansion is

(a+b)^3=1a^3+3a^2b+3ab^2+1b^3
sashaice [31]2 years ago
5 0

Answer:

Required coefficient :coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

Explanation:  

Formula for binomial expansion is (a+b)^n=^nC_0\cdot a^n\cdot b^0+^nC_1\cdota^(n-1)\cdot b^1+------b^n

We will substitute the values a=a, b=b and n=3  in the formula for binomial expansion we will get

^3C_0\cdot a^3\cdot b^0+^3C_1\cdot a^2\cdot b^1+^3C_2\cdot a^1\cdot b^2+^3C_3\cdot a^0\cdot b^3

After simplification of the terms we will get

a^3+3\cdot a^2\cdot b+3\cdot a\cdot b^2+b^3

Since, ^nC_r=\frac{n!}{(r!)(n-r)!}

Therefore the required coefficient : coefficients of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.

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Looking at the ratio given in this question, we know that there are 1 1/2 (3 /2) more children than adults on the line to watch the new superhero movie.

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