Answer
$$(4x+1)^4=256x^4+256x^3+96x^2+16x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x+1)^4& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}256x^4+256x^3+96x^2+16x+1\end{aligned} $$ | |
| ① | $$ (4x+1)^4 = (4x+1)^2 \cdot (4x+1)^2 $$ |
| ② | Find $ \left(4x+1\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 4x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(4x+1\right)^2 = \color{blue}{\left( 4x \right)^2} +2 \cdot 4x \cdot 1 + \color{red}{1^2} = 16x^2+8x+1\end{aligned} $$ |
| ③ | Multiply each term of $ \left( \color{blue}{16x^2+8x+1}\right) $ by each term in $ \left( 16x^2+8x+1\right) $. $$ \left( \color{blue}{16x^2+8x+1}\right) \cdot \left( 16x^2+8x+1\right) = 256x^4+128x^3+16x^2+128x^3+64x^2+8x+16x^2+8x+1 $$ |
| ④ | Combine like terms: $$ 256x^4+ \color{blue}{128x^3} + \color{red}{16x^2} + \color{blue}{128x^3} + \color{green}{64x^2} + \color{orange}{8x} + \color{green}{16x^2} + \color{orange}{8x} +1 = \\ = 256x^4+ \color{blue}{256x^3} + \color{green}{96x^2} + \color{orange}{16x} +1 $$ |
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