Question

Consider the expansion of (x + 2y)^10. Determine the coefficients for the terms with the powers of x and y shown.

Answer 1

Answer with Step-by-step explanation:

We are given that  an expression

$(x+2y)^{10}$

Binomial expansion o f $(x+y)^n$ is given by

=$nC_0 x^n+nC_1x^{n-1}y^1+nC_2x^{n-2}y^2+nC_3x^{n-3}y^3+... nC_n y^n$

a. We have to find the coefficient of $x^2y^8$

$(x+2y)^{10}=10C_0x^{10}+10C_1x^9(2y)+10C_2x^8(2y)^2+10C_3x^7(2y)^3+...+10C_{10}(2y)^{10}$

Term is $10C_8x^(2y)^8$

Coefficient =$10C_8\cdot 2^8$

b.Term in which $x^4y^6$  is $10C_6x^4(2y)^6$

Coefficient =$10C_4\cdot 2^6$

c.We have to find the coefficient of $x^5y^5$

Term  is $10C_5x^5(2y)^5$

Coefficient =$10C_5\cdot 2^5$

Answer 2

Answer:

Step-by-step explanation: