how do we solve this bionomial theorem

Question

(x²y+a/2)^7

Answer 1

The expansion of (a+b)^7 using the binomial theorem is a^7+7a^6b+(7*6/2)*a^5b^2+(7*6*5/6)*a^4b^3+... Let's calculate the coefficients: 1, 7, 21, 35, 35, 21, 7, 1. Substituting the values in the question for a and b we have a=x^2y and b=a/2:

x^14y^7+7x^12y^6*a/2+21x^10y^5a^2/4+35x^8y^4a^3/8+35x^6y^3a^4/16+21x^4y^2a^5/32+7x^2ya^6/64+a^7/128.