Question
Answer
$$(5x^2+8)^4x^2=625x^{10}+4000x^8+9600x^6+10240x^4+4096x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x^2+8)^4x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(625x^8+4000x^6+9600x^4+10240x^2+4096)x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}625x^{10}+4000x^8+9600x^6+10240x^4+4096x^2\end{aligned} $$ | |
| ① | $$ (5x^2+8)^4 = (5x^2+8)^2 \cdot (5x^2+8)^2 $$ |
| ② | Find $ \left(5x^2+8\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5x^2 } $ and $ B = \color{red}{ 8 }$. $$ \begin{aligned}\left(5x^2+8\right)^2 = \color{blue}{\left( 5x^2 \right)^2} +2 \cdot 5x^2 \cdot 8 + \color{red}{8^2} = 25x^4+80x^2+64\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{25x^4+80x^2+64}\right) $ by each term in $ \left( 25x^4+80x^2+64\right) $. $$ \left( \color{blue}{25x^4+80x^2+64}\right) \cdot \left( 25x^4+80x^2+64\right) = \\ = 625x^8+2000x^6+1600x^4+2000x^6+6400x^4+5120x^2+1600x^4+5120x^2+4096 $$ |
| ④ | Combine like terms: $$ 625x^8+ \color{blue}{2000x^6} + \color{red}{1600x^4} + \color{blue}{2000x^6} + \color{green}{6400x^4} + \color{orange}{5120x^2} + \color{green}{1600x^4} + \color{orange}{5120x^2} +4096 = \\ = 625x^8+ \color{blue}{4000x^6} + \color{green}{9600x^4} + \color{orange}{10240x^2} +4096 $$ |
| ⑤ | $$ \left( \color{blue}{625x^8+4000x^6+9600x^4+10240x^2+4096}\right) \cdot x^2 = 625x^{10}+4000x^8+9600x^6+10240x^4+4096x^2 $$ |
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