Answer:
[tex]f(x)\cdot g(x)=x^3-21x^2+135x-243[/tex]
Step-by-step explanation:
We are given the two functions:
[tex]f(x)=x^2-12x+27\text{ and } g(x)=x-9[/tex]
And we want to find:
[tex]f(x)\cdot g(x)[/tex]
So, by substitution:
[tex]=(x^2-12x+27)\cdot (x-9)[/tex]
Distribute:
[tex]=(x^2-12x+27)(x)+(x^2-12x+27)(-9)[/tex]
Multiply:
[tex]=(x^3-12x^2+27x)+(-9x^2+108x-243)[/tex]
Rearrange:
[tex]=(x^3)+(-12x^2-9x^2)+(27x+108x)+(-243)[/tex]
Combine like terms:
[tex]=x^3-21x^2+135x-243[/tex]
Hence:
[tex]f(x)\cdot g(x)=x^3-21x^2+135x-243[/tex]
