Question
Answer
$$(m-4)^4=m^4-16m^3+96m^2-256m+256$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(m-4)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}m^4-16m^3+96m^2-256m+256\end{aligned} $$ | |
| ① | $$ (m-4)^4 = (m-4)^2 \cdot (m-4)^2 $$ |
| ② | Find $ \left(m-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}{ m } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(m-4\right)^2 = \color{blue}{m^2} -2 \cdot m \cdot 4 + \color{red}{4^2} = m^2-8m+16\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{m^2-8m+16}\right) $ by each term in $ \left( m^2-8m+16\right) $. $$ \left( \color{blue}{m^2-8m+16}\right) \cdot \left( m^2-8m+16\right) = m^4-8m^3+16m^2-8m^3+64m^2-128m+16m^2-128m+256 $$ |
| ④ | Combine like terms: $$ m^4 \color{blue}{-8m^3} + \color{red}{16m^2} \color{blue}{-8m^3} + \color{green}{64m^2} \color{orange}{-128m} + \color{green}{16m^2} \color{orange}{-128m} +256 = \\ = m^4 \color{blue}{-16m^3} + \color{green}{96m^2} \color{orange}{-256m} +256 $$ |
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