Given:
The function
[tex]\begin{gathered} f(x)=\sqrt{x^2+12x+36} \\ g(x)=x^3-12 \end{gathered}[/tex]
Required:
[tex]\text{ Which expression is equal to }f(x)\cdot g(x)?[/tex]
Explanation:
The calculation is as:
[tex]\begin{gathered} \text{ We can write }f(x)\text{ as }:\text{ } \\ f(x)=\sqrt{x^2+12x+36} \\ =\sqrt{(x+6)^2} \\ =x+6 \end{gathered}[/tex]
Now,
[tex]\begin{gathered} f(x)\cdot g(x)=(x+6)(x^3-12) \\ =x^4-12x+6x^3-72 \\ =x^4+6x^3-12x-72 \end{gathered}[/tex]
Answer:
