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