Question
Answer
$$(x^2-2xwcos\cdot105+w^2)(x^2-2xwcos\cdot135+w^2)=56700c^2o^2s^2w^2x^2-480cosw^3x-480coswx^3+w^4+2w^2x^2+x^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-2xwcos\cdot105+w^2)(x^2-2xwcos\cdot135+w^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-210coswx+w^2)(x^2-270coswx+w^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}56700c^2o^2s^2w^2x^2-480cosw^3x-480coswx^3+w^4+2w^2x^2+x^4\end{aligned} $$ | |
| ① | $$ 2 x w c o s \cdot 105 = 210 c o s w x $$$$ 2 x w c o s \cdot 135 = 270 c o s w x $$ |
| ② | Multiply each term of $ \left( \color{blue}{x^2-210coswx+w^2}\right) $ by each term in $ \left( x^2-270coswx+w^2\right) $. $$ \left( \color{blue}{x^2-210coswx+w^2}\right) \cdot \left( x^2-270coswx+w^2\right) = \\ = x^4-270coswx^3+w^2x^2-210coswx^3+56700c^2o^2s^2w^2x^2-210cosw^3x+w^2x^2-270cosw^3x+w^4 $$ |
| ③ | Combine like terms: $$ x^4 \color{blue}{-270coswx^3} + \color{red}{w^2x^2} \color{blue}{-210coswx^3} +56700c^2o^2s^2w^2x^2 \color{green}{-210cosw^3x} + \color{red}{w^2x^2} \color{green}{-270cosw^3x} +w^4 = \\ = 56700c^2o^2s^2w^2x^2 \color{green}{-480cosw^3x} \color{blue}{-480coswx^3} +w^4+ \color{red}{2w^2x^2} +x^4 $$ |
This page was created using
Simplify polynomials calculator