Answer:
Option (C)
Step-by-step explanation:
Given : f(x) = [tex]\sqrt{x^2+12x+36}[/tex]
g(x) = x³ - 12
f(x).g(x) = f(x) × g(x)
= [tex](\sqrt{x^2+12x+36})\times (x^3-12)[/tex]
= [tex](\sqrt{(x+6)^2})\times (x^3-12)[/tex]
= (x + 6)(x³ - 12)
= x(x³ - 12) + 6(x³ - 12) [Distributive property]
= x⁴ - 12x + 6x³ - 72
= x⁴ + 6x³ - 12x - 72
Therefore, option (C) will be the answer.
