Answer:
The coefficient of x²y³ is 40.
Step-by-step explanation:
The binomial expansion is defined as
[tex](a+b)^n=^nC_0a^n+^nC_1a^{n-1}b+...+^nC_ra^rb^{n-r}+....+^nC_nb^n[/tex]
The expression is
[tex](2x+y)^5[/tex]
Expand the binomial expansion.
[tex](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[/tex]
Combination formula:
[tex]^nC_r=\frac{n!}{r!(n-r)!}[/tex]
[tex](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[/tex]
Therefore the coefficient of x²y³ is 40.
