Question

PLATO;
can somebody please help me with the following question below:

Answer 1

`\bf \begin{cases} f(x) = &x-6\\ g(x) = &x^{(1)/(2)}(x+3)\\ &√(x)(x+3)\\ &x√(x)+3√(x) \end{cases} \\\\\\ f(x) * g(x)\implies \begin{array}{rllll} x√(x)+3√(x)\\\\ * x\\\cline{1-1} x^2√(x)+3x√(x) \end{array}\qquad +\qquad \begin{array}{rllll} x√(x)+3√(x)\\\\ * -6\\\cline{1-1} -6x√(x)-18√(x) \end{array}`

`\bf x^2√(x)\stackrel{like-terms}{+3x√(x)-6x√(x)}-18√(x)\implies x^2√(x)-3x√(x)-18√(x) \\\\\\ √((x^2)^2 x)-3√(x^2 x)-18√(x)\implies √(x^4 x)-3√(x^2 x)-18√(x) \\\\\\ \sqrt{x^(4+1)}-3\sqrt{x^(2+1)}-18√(x)\implies \boxed{√(x^5)-3√(x^3)-18√(x)}`