Answer:
a = 21
b = 3
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{11cm}\underline{Binomial Series}\\\\$\displaystyle (a+b)^n=a^n+\binom{n}{1}a^{n-1}b^1+\binom{n}{2}a^{n-2}b^2+...+\binom{n}{r}a^{n-r}b^r+...+b^n$\\\\\\Where $\displaystyle \binom{n}{r} \: = \:^{n}\text{C}_{r} = \frac{n!}{r!(n-r)!}$\\\end{minipage}}[/tex]
Given binomial expansion:
[tex](x+y)^7=x^7+7x^6y+ax^5y^2+35x^4y^b+35x^3y^4+21x^2y^5+7xy^6+y^7[/tex]
The coefficients of the given binomial expansion are:
- 1, 7, a, 35, 35, 21, 7, 1
Due to the symmetry of the coefficients in a binomial expansion:
The exponent of the second term y increases by one for each term in the expansion. Therefore:
