Answer:
1. x^2−16
2. x^3+27
3. x^3−4x^2
4. x^2−9
Explanation: Step-by-step
1. Let's simplify step-by-step.
x2−16
There are no like terms.
2. Let's simplify step-by-step.
x3+27
There are no like terms.
3. Let's simplify step-by-step.
x3−4x2
There are no like terms.
4.Let's simplify step-by-step.
x2−9
There are no like terms.
[tex]\bf \cfrac{x^2-16}{x^3-4x^2}\implies \cfrac{\stackrel{\textit{difference of squares}}{x^2-4^2}}{x^2(x-4)}\implies \cfrac{~~\begin{matrix} (x-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x+4)}{x^2~~\begin{matrix} (x-4) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x+4}{x^2} \\\\[-0.35em] ~\dotfill\\\\ \cfrac{x^3+27}{x^2-9}\implies \cfrac{\stackrel{\textit{sum of cubics}}{x^3+3^3}}{\underset{\textit{difference of squares}}{x^2-3^2}}[/tex]
[tex]\bf \cfrac{~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~(x^2-3x+3^2)}{(x-3)~~\begin{matrix} (x+3) \\[-0.7em]\cline{1-1}\\[-5pt]\end{matrix}~~}\implies \cfrac{x^2-3x+9}{x-3}[/tex]
