Answer
$x^3+4x^2-15x-18$
Work Step by Step
Grouping the first two factors and then using the FOIL Method which is given by $(a+b)(c+d)=ac+ad+bc+bd,$ the given expression, $
(x-3)(x+6)(x+1)
,$ is equivalent to
\begin{align*}
&
[(x-3)(x+6)](x+1)
\\&=
[x(x)+x(6)-3(x)-3(6)](x+1)
\\&=
[x^2+6x-3x-18](x+1)
\\&=
(x^2+3x-18)(x+1)
.\end{align*}
Using the Distributive Property which is given by $a(b+c)=ab+ac,$ the expression above is equivalent to
\begin{align*}
&
x^2(x)+x^2(1)+3x(x)+3x(1)-18(x)-18(1)
\\&=
x^3+x^2+3x^2+3x-18x-18
\\&=
x^3+4x^2-15x-18
.\end{align*}
Hence, the product of the given expression is $
x^3+4x^2-15x-18
$.
