Given, (1−y)m(1+y)n=1+a1y+a2y2+...+am+nym+n Now, (1−y)m(1+y)n=(1−my+mC2y2+...+ (−1)m⋅mCmym) ×(1+ny+nC2y2+..+nCnyn) On expanding, (1−y)m(1+y)n=1+(n−m)y +(nC2−mn+mC2)y2+...
∴ Coefficient of y=n−m Coefficient of y2=nC2−mn+mC2 Given expression have Coefficient of y=a1=10 Coefficient of y2=a2=10 ∴n−m=10⋅⋅⋅⋅⋅⋅⋅(i) and nC2+mC2−mn=10⋅⋅⋅⋅⋅⋅⋅(ii) From Eq. (ii),