Question
Answer
$$(5+4x-x^2)^2=x^4-8x^3+6x^2+40x+25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5+4x-x^2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^4-8x^3+6x^2+40x+25\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{5+4x-x^2}\right) $ by each term in $ \left( 5+4x-x^2\right) $. $$ \left( \color{blue}{5+4x-x^2}\right) \cdot \left( 5+4x-x^2\right) = 25+20x-5x^2+20x+16x^2-4x^3-5x^2-4x^3+x^4 $$ |
| ② | Combine like terms: $$ 25+ \color{blue}{20x} \color{red}{-5x^2} + \color{blue}{20x} + \color{green}{16x^2} \color{orange}{-4x^3} \color{green}{-5x^2} \color{orange}{-4x^3} +x^4 = \\ = x^4 \color{orange}{-8x^3} + \color{green}{6x^2} + \color{blue}{40x} +25 $$ |
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