Question
Answer
$$(a-3)^4=a^4-12a^3+54a^2-108a+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a-3)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}a^4-12a^3+54a^2-108a+81\end{aligned} $$ | |
| ① | $$ (a-3)^4 = (a-3)^2 \cdot (a-3)^2 $$ |
| ② | Find $ \left(a-3\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}{ 3 }$. $$ \begin{aligned}\left(a-3\right)^2 = \color{blue}{a^2} -2 \cdot a \cdot 3 + \color{red}{3^2} = a^2-6a+9\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{a^2-6a+9}\right) $ by each term in $ \left( a^2-6a+9\right) $. $$ \left( \color{blue}{a^2-6a+9}\right) \cdot \left( a^2-6a+9\right) = a^4-6a^3+9a^2-6a^3+36a^2-54a+9a^2-54a+81 $$ |
| ④ | Combine like terms: $$ a^4 \color{blue}{-6a^3} + \color{red}{9a^2} \color{blue}{-6a^3} + \color{green}{36a^2} \color{orange}{-54a} + \color{green}{9a^2} \color{orange}{-54a} +81 = \\ = a^4 \color{blue}{-12a^3} + \color{green}{54a^2} \color{orange}{-108a} +81 $$ |
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