Question
Answer
$$(2z^2-2x)^4=16z^8-64xz^6+96x^2z^4-64x^3z^2+16x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2z^2-2x)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}16z^8-64xz^6+96x^2z^4-64x^3z^2+16x^4\end{aligned} $$ | |
| ① | $$ (2z^2-2x)^4 = (2z^2-2x)^2 \cdot (2z^2-2x)^2 $$ |
| ② | Find $ \left(2z^2-2x\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^2 } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(2z^2-2x\right)^2 = \color{blue}{\left( 2z^2 \right)^2} -2 \cdot 2z^2 \cdot 2x + \color{red}{\left( 2x \right)^2} = 4z^4-8xz^2+4x^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4z^4-8xz^2+4x^2}\right) $ by each term in $ \left( 4z^4-8xz^2+4x^2\right) $. $$ \left( \color{blue}{4z^4-8xz^2+4x^2}\right) \cdot \left( 4z^4-8xz^2+4x^2\right) = \\ = 16z^8-32xz^6+16x^2z^4-32xz^6+64x^2z^4-32x^3z^2+16x^2z^4-32x^3z^2+16x^4 $$ |
| ④ | Combine like terms: $$ 16z^8 \color{blue}{-32xz^6} + \color{red}{16x^2z^4} \color{blue}{-32xz^6} + \color{green}{64x^2z^4} \color{orange}{-32x^3z^2} + \color{green}{16x^2z^4} \color{orange}{-32x^3z^2} +16x^4 = \\ = 16z^8 \color{blue}{-64xz^6} + \color{green}{96x^2z^4} \color{orange}{-64x^3z^2} +16x^4 $$ |
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