Answer
$$(x+2.762)(x+4.098)(x-4.098)=x^3+2x^2-16x-32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+2.762)(x+4.098)(x-4.098)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+4x+2x+8)(x-4.098) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+6x+8)(x-4.098) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-4x^2+6x^2-24x+8x-32 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3+2x^2-16x-32\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x+4\right) = x^2+4x+2x+8 $$ |
| ② | Combine like terms: $$ x^2+ \color{blue}{4x} + \color{blue}{2x} +8 = x^2+ \color{blue}{6x} +8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2+6x+8}\right) $ by each term in $ \left( x-4\right) $. $$ \left( \color{blue}{x^2+6x+8}\right) \cdot \left( x-4\right) = x^3-4x^2+6x^2-24x+8x-32 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-4x^2} + \color{blue}{6x^2} \color{red}{-24x} + \color{red}{8x} -32 = x^3+ \color{blue}{2x^2} \color{red}{-16x} -32 $$ |
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