Question
Answer
$$(x^4+14x^3+63x^2+98x+28)^2=x^8+28x^7+322x^6+1960x^5+6769x^4+13132x^3+13132x^2+5488x+784$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^4+14x^3+63x^2+98x+28)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^8+28x^7+322x^6+1960x^5+6769x^4+13132x^3+13132x^2+5488x+784\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^4+14x^3+63x^2+98x+28}\right) $ by each term in $ \left( x^4+14x^3+63x^2+98x+28\right) $. $$ \left( \color{blue}{x^4+14x^3+63x^2+98x+28}\right) \cdot \left( x^4+14x^3+63x^2+98x+28\right) = \\ = x^8+14x^7+63x^6+98x^5+28x^4+14x^7+196x^6+882x^5+1372x^4+392x^3+63x^6+882x^5+3969x^4+6174x^3+1764x^2+98x^5+1372x^4+6174x^3+9604x^2+2744x+28x^4+392x^3+1764x^2+2744x+784 $$ |
| ② | Combine like terms: $$ x^8+ \color{blue}{14x^7} + \color{red}{63x^6} + \color{green}{98x^5} + \color{orange}{28x^4} + \color{blue}{14x^7} + \color{blue}{196x^6} + \color{red}{882x^5} + \color{green}{1372x^4} + \color{orange}{392x^3} + \color{blue}{63x^6} + \color{blue}{882x^5} + \color{red}{3969x^4} + \color{green}{6174x^3} + \color{orange}{1764x^2} + \color{blue}{98x^5} + \color{blue}{1372x^4} + \color{red}{6174x^3} + \color{green}{9604x^2} + \color{orange}{2744x} + \color{blue}{28x^4} + \color{red}{392x^3} + \color{green}{1764x^2} + \color{orange}{2744x} +784 = \\ = x^8+ \color{blue}{28x^7} + \color{blue}{322x^6} + \color{blue}{1960x^5} + \color{blue}{6769x^4} + \color{red}{13132x^3} + \color{green}{13132x^2} + \color{orange}{5488x} +784 $$ |
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