Question

What is the coefficient of x^2y^3 in the expansion of (2x+y)^5

Answer 1

Answer:40

Explanation:

algebra 2 test

Answer 2

The coefficient of x²y³ is 40.

Explanation:

The binomial expansion is defined as

`(a+b)^n=^nC_0a^n+^nC_1a^(n-1)b+...+^nC_ra^rb^(n-r)+....+^nC_nb^n`

The expression is

`(2x+y)^5`

Expand the binomial expansion.

`(2x+y)^5=^5C_0(2x)^5+^5C_1(2x)^(4)(y)+^5C_2(2x)^(3)(y)^2+^5C_3(2x)^(2)(y)^3+^5C_4(2x)^(1)(y)^4+^5C_5(y)^5`

Combination formula:

`^nC_r=(n!)/(r!(n-r)!)`

`(2x+y)^5=32 x^5 + 80 x^4 y + 80 x^3 y^2 + 40 x^2 y^3 + 10 x y^4 + y^5`

Therefore the coefficient of x²y³ is 40.