Question
Answer
$$(5x^2+3)^4x^2=625x^{10}+1500x^8+1350x^6+540x^4+81x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5x^2+3)^4x^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(625x^8+1500x^6+1350x^4+540x^2+81)x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}625x^{10}+1500x^8+1350x^6+540x^4+81x^2\end{aligned} $$ | |
| ① | $$ (5x^2+3)^4 = (5x^2+3)^2 \cdot (5x^2+3)^2 $$ |
| ② | Find $ \left(5x^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}{ 5x^2 } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(5x^2+3\right)^2 = \color{blue}{\left( 5x^2 \right)^2} +2 \cdot 5x^2 \cdot 3 + \color{red}{3^2} = 25x^4+30x^2+9\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{25x^4+30x^2+9}\right) $ by each term in $ \left( 25x^4+30x^2+9\right) $. $$ \left( \color{blue}{25x^4+30x^2+9}\right) \cdot \left( 25x^4+30x^2+9\right) = \\ = 625x^8+750x^6+225x^4+750x^6+900x^4+270x^2+225x^4+270x^2+81 $$ |
| ④ | Combine like terms: $$ 625x^8+ \color{blue}{750x^6} + \color{red}{225x^4} + \color{blue}{750x^6} + \color{green}{900x^4} + \color{orange}{270x^2} + \color{green}{225x^4} + \color{orange}{270x^2} +81 = \\ = 625x^8+ \color{blue}{1500x^6} + \color{green}{1350x^4} + \color{orange}{540x^2} +81 $$ |
| ⑤ | $$ \left( \color{blue}{625x^8+1500x^6+1350x^4+540x^2+81}\right) \cdot x^2 = 625x^{10}+1500x^8+1350x^6+540x^4+81x^2 $$ |
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