Answer:
Required coefficient :coefficient of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.
Explanation:
Formula for binomial expansion is [tex](a+b)^n=^nC_0\cdot a^n\cdot b^0+^nC_1\cdota^(n-1)\cdot b^1+------b^n[/tex]
We will substitute the values a=a, b=b and n=3 in the formula for binomial expansion we will get
[tex]^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[/tex]
After simplification of the terms we will get
[tex]a^3+3\cdot a^2\cdot b+3\cdot a\cdot b^2+b^3[/tex]
Since, [tex]^nC_r=\frac{n!}{(r!)(n-r)!}[/tex]
Therefore the required coefficient : coefficients of 1st, 2nd, 3rd and 4th term are 1, 3,3,1 respectively.
