If 2 x^2+5 x+6 (x+2)^3 = a x+2 + b (x+2)^2 + c (x+2)^3 then a . b + b . c + c . a =

Step-by-step solution

aligned & Given 2 x^2+5 x+6 (x+2)^3 = a (x+2) + b (x+2)^2 + c (x+3)^3 & 2 x^2+5 x+6=a(x+2)^2+b(x+2)+c & 2 x^2+5 x+6=x^2(a)+x(4 a+b)+(4 a+2 b+c) aligned Comparing we get, a=2, b=-3, c=4 Hence a b+b c+c a=-10