Question
Answer
$$(x^3+x^2+5x+4)^2=x^6+2x^5+11x^4+18x^3+33x^2+40x+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^3+x^2+5x+4)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^6+2x^5+11x^4+18x^3+33x^2+40x+16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3+x^2+5x+4}\right) $ by each term in $ \left( x^3+x^2+5x+4\right) $. $$ \left( \color{blue}{x^3+x^2+5x+4}\right) \cdot \left( x^3+x^2+5x+4\right) = \\ = x^6+x^5+5x^4+4x^3+x^5+x^4+5x^3+4x^2+5x^4+5x^3+25x^2+20x+4x^3+4x^2+20x+16 $$ |
| ② | Combine like terms: $$ x^6+ \color{blue}{x^5} + \color{red}{5x^4} + \color{green}{4x^3} + \color{blue}{x^5} + \color{orange}{x^4} + \color{blue}{5x^3} + \color{red}{4x^2} + \color{orange}{5x^4} + \color{green}{5x^3} + \color{orange}{25x^2} + \color{blue}{20x} + \color{green}{4x^3} + \color{orange}{4x^2} + \color{blue}{20x} +16 = \\ = x^6+ \color{blue}{2x^5} + \color{orange}{11x^4} + \color{green}{18x^3} + \color{orange}{33x^2} + \color{blue}{40x} +16 $$ |
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