Question
Answer
$$(a+0.5)^4=a^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(a+0.5)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}a^4\end{aligned} $$ | |
| ① | $$ (a0)^4 = (a0)^2 \cdot (a0)^2 $$ |
| ② | Find $ \left(a+0\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}{ 0 }$. $$ \begin{aligned}\left(a+0\right)^2 = \color{blue}{a^2} +2 \cdot a \cdot 0 + \color{red}{0^2} = a^20a0\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{a^20a0}\right) $ by each term in $ \left( a^20a0\right) $. $$ \left( \color{blue}{a^20a0}\right) \cdot \left( a^20a0\right) = \\ = a^4 \cancel{0a^3} \cancel{0a^2} \cancel{0a^3} \cancel{0a^2} \cancel{0a} \cancel{0a^2} \cancel{0a}0 $$ |
| ④ | Combine like terms: $$ a^4 \, \color{blue}{ \cancel{0a^3}} \, \, \color{green}{ \cancel{0a^2}} \, \, \color{blue}{ \cancel{0a^3}} \, \, \color{blue}{ \cancel{0a^2}} \, \, \color{green}{ \cancel{0a}} \, \, \color{blue}{ \cancel{0a^2}} \, \, \color{green}{ \cancel{0a}} \,0 = a^4 $$ |
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