Question
Answer
$$(x^1+x^3+x^3+x^{16})^2=x^{32}+4x^{19}+2x^{17}+4x^6+4x^4+x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^1+x^3+x^3+x^{16})^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^{16}+2x^3+x)^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^{32}+4x^{19}+2x^{17}+4x^6+4x^4+x^2\end{aligned} $$ | |
| ① | Combine like terms: $$ x+ \color{blue}{x^3} + \color{blue}{x^3} +x^{16} = x^{16}+ \color{blue}{2x^3} +x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^{16}+2x^3+x}\right) $ by each term in $ \left( x^{16}+2x^3+x\right) $. $$ \left( \color{blue}{x^{16}+2x^3+x}\right) \cdot \left( x^{16}+2x^3+x\right) = \\ = x^{32}+2x^{19}+x^{17}+2x^{19}+4x^6+2x^4+x^{17}+2x^4+x^2 $$ |
| ③ | Combine like terms: $$ x^{32}+ \color{blue}{2x^{19}} + \color{red}{x^{17}} + \color{blue}{2x^{19}} +4x^6+ \color{green}{2x^4} + \color{red}{x^{17}} + \color{green}{2x^4} +x^2 = \\ = x^{32}+ \color{blue}{4x^{19}} + \color{red}{2x^{17}} +4x^6+ \color{green}{4x^4} +x^2 $$ |
This page was created using
Simplify polynomials calculator