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