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