What is the fourth term in the expansion of the binomial #(2x+y^2)^5#?
1 Answer
Jun 27, 2017
Explanation:
#"using the "color(blue)"binomial theorem"#
#• (x+y)^n=sum_(r=0)^n((n),(r))x^(n-r)y^r#
#"where " ((n),(r))=(n!)/(r!(n-r)!)#
#"the general term is " ((n),(r))x^(n-r)y^r#
#"and " T_(r+1)=((n),(r))x^(n-r)y^r#
#"here " x=2x" and " y=y^2#
#• color(blue)" for fourth term use r=3"#
#rArrT_4=((5),(3))(2x)^2(y^2)^3#
#color(white)(rArrT_4)=10xx4x^2xxy^6#
#color(white)(rArrT_4)=40x^2y^6#
