Answer with Step-by-step explanation:
We are given that an expression
[tex](x+2y)^{10}[/tex]
Binomial expansion o f [tex](x+y)^n[/tex] is given by
=[tex]nC_0 x^n+nC_1x^{n-1}y^1+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+... nC_n y^n[/tex]
a. We have to find the coefficient of [tex]x^2y^8[/tex]
[tex](x+2y)^{10}=10C_0x^{10}+10C_1x^9(2y)+10C_2x^8(2y)^2+10C_3x^7(2y)^3+...+10C_{10}(2y)^{10}[/tex]
Term is [tex]10C_8x^(2y)^8[/tex]
Coefficient =[tex]10C_8\cdot 2^8[/tex]
b.Term in which [tex]x^4y^6[/tex] is [tex]10C_6x^4(2y)^6[/tex]
Coefficient =[tex]10C_4\cdot 2^6[/tex]
c.We have to find the coefficient of [tex]x^5y^5[/tex]
Term is [tex]10C_5x^5(2y)^5[/tex]
Coefficient =[tex]10C_5\cdot 2^5[/tex]
