Question

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

a. x^2y^8
b. x^4y^6
c. x^5y^5

Answer 1

Explanation:

Answer 2

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`