Question
Answer
$$-3+(2x-4)^4=16x^4-128x^3+384x^2-512x+253$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-3+(2x-4)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-3+16x^4-128x^3+384x^2-512x+256 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}16x^4-128x^3+384x^2-512x+253\end{aligned} $$ | |
| ① | $$ (2x-4)^4 = (2x-4)^2 \cdot (2x-4)^2 $$ |
| ② | Find $ \left(2x-4\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(2x-4\right)^2 = \color{blue}{\left( 2x \right)^2} -2 \cdot 2x \cdot 4 + \color{red}{4^2} = 4x^2-16x+16\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{4x^2-16x+16}\right) $ by each term in $ \left( 4x^2-16x+16\right) $. $$ \left( \color{blue}{4x^2-16x+16}\right) \cdot \left( 4x^2-16x+16\right) = 16x^4-64x^3+64x^2-64x^3+256x^2-256x+64x^2-256x+256 $$ |
| ④ | Combine like terms: $$ 16x^4 \color{blue}{-64x^3} + \color{red}{64x^2} \color{blue}{-64x^3} + \color{green}{256x^2} \color{orange}{-256x} + \color{green}{64x^2} \color{orange}{-256x} +256 = \\ = 16x^4 \color{blue}{-128x^3} + \color{green}{384x^2} \color{orange}{-512x} +256 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{-3} +16x^4-128x^3+384x^2-512x+ \color{blue}{256} = 16x^4-128x^3+384x^2-512x+ \color{blue}{253} $$ |
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