Question
Answer
$$(t+2)^4=t^4+8t^3+24t^2+32t+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(t+2)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}t^4+8t^3+24t^2+32t+16\end{aligned} $$ | |
| ① | $$ (t+2)^4 = (t+2)^2 \cdot (t+2)^2 $$ |
| ② | Find $ \left(t+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ t } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(t+2\right)^2 = \color{blue}{t^2} +2 \cdot t \cdot 2 + \color{red}{2^2} = t^2+4t+4\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{t^2+4t+4}\right) $ by each term in $ \left( t^2+4t+4\right) $. $$ \left( \color{blue}{t^2+4t+4}\right) \cdot \left( t^2+4t+4\right) = t^4+4t^3+4t^2+4t^3+16t^2+16t+4t^2+16t+16 $$ |
| ④ | Combine like terms: $$ t^4+ \color{blue}{4t^3} + \color{red}{4t^2} + \color{blue}{4t^3} + \color{green}{16t^2} + \color{orange}{16t} + \color{green}{4t^2} + \color{orange}{16t} +16 = \\ = t^4+ \color{blue}{8t^3} + \color{green}{24t^2} + \color{orange}{32t} +16 $$ |
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