Question
Answer
$$(5+2z^2)^4=16z^8+160z^6+600z^4+1000z^2+625$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5+2z^2)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16z^8+160z^6+600z^4+1000z^2+625\end{aligned} $$ | |
| ① | $$ (5+2z^2)^4 = (5+2z^2)^2 \cdot (5+2z^2)^2 $$ |
| ② | Find $ \left(5+2z^2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5 } $ and $ B = \color{red}{ 2z^2 }$. $$ \begin{aligned}\left(5+2z^2\right)^2 = \color{blue}{5^2} +2 \cdot 5 \cdot 2z^2 + \color{red}{\left( 2z^2 \right)^2} = 25+20z^2+4z^4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{25+20z^2+4z^4}\right) $ by each term in $ \left( 25+20z^2+4z^4\right) $. $$ \left( \color{blue}{25+20z^2+4z^4}\right) \cdot \left( 25+20z^2+4z^4\right) = \\ = 625+500z^2+100z^4+500z^2+400z^4+80z^6+100z^4+80z^6+16z^8 $$ |
| ④ | Combine like terms: $$ 625+ \color{blue}{500z^2} + \color{red}{100z^4} + \color{blue}{500z^2} + \color{green}{400z^4} + \color{orange}{80z^6} + \color{green}{100z^4} + \color{orange}{80z^6} +16z^8 = \\ = 16z^8+ \color{orange}{160z^6} + \color{green}{600z^4} + \color{blue}{1000z^2} +625 $$ |
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