Question
Answer
$$(x^2+3)^4=x^8+12x^6+54x^4+108x^2+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+3)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^8+12x^6+54x^4+108x^2+81\end{aligned} $$ | |
| ① | $$ (x^2+3)^4 = (x^2+3)^2 \cdot (x^2+3)^2 $$ |
| ② | Find $ \left(x^2+3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x^2 } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(x^2+3\right)^2 = \color{blue}{\left( x^2 \right)^2} +2 \cdot x^2 \cdot 3 + \color{red}{3^2} = x^4+6x^2+9\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4+6x^2+9}\right) $ by each term in $ \left( x^4+6x^2+9\right) $. $$ \left( \color{blue}{x^4+6x^2+9}\right) \cdot \left( x^4+6x^2+9\right) = x^8+6x^6+9x^4+6x^6+36x^4+54x^2+9x^4+54x^2+81 $$ |
| ④ | Combine like terms: $$ x^8+ \color{blue}{6x^6} + \color{red}{9x^4} + \color{blue}{6x^6} + \color{green}{36x^4} + \color{orange}{54x^2} + \color{green}{9x^4} + \color{orange}{54x^2} +81 = \\ = x^8+ \color{blue}{12x^6} + \color{green}{54x^4} + \color{orange}{108x^2} +81 $$ |
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