Question
Answer
$$(h+t)^4=h^4+4h^3t+6h^2t^2+4ht^3+t^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(h+t)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}h^4+4h^3t+6h^2t^2+4ht^3+t^4\end{aligned} $$ | |
| ① | $$ (h+t)^4 = (h+t)^2 \cdot (h+t)^2 $$ |
| ② | Find $ \left(h+t\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ h } $ and $ B = \color{red}{ t }$. $$ \begin{aligned}\left(h+t\right)^2 = \color{blue}{h^2} +2 \cdot h \cdot t + \color{red}{t^2} = h^2+2ht+t^2\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{h^2+2ht+t^2}\right) $ by each term in $ \left( h^2+2ht+t^2\right) $. $$ \left( \color{blue}{h^2+2ht+t^2}\right) \cdot \left( h^2+2ht+t^2\right) = \\ = h^4+2h^3t+h^2t^2+2h^3t+4h^2t^2+2ht^3+h^2t^2+2ht^3+t^4 $$ |
| ④ | Combine like terms: $$ h^4+ \color{blue}{2h^3t} + \color{red}{h^2t^2} + \color{blue}{2h^3t} + \color{green}{4h^2t^2} + \color{orange}{2ht^3} + \color{green}{h^2t^2} + \color{orange}{2ht^3} +t^4 = \\ = h^4+ \color{blue}{4h^3t} + \color{green}{6h^2t^2} + \color{orange}{4ht^3} +t^4 $$ |
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