Question
Answer
$$(x^2-5)(x^2-7)(x^2-35)=x^6-47x^4+455x^2-1225$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2-5)(x^2-7)(x^2-35)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^4-7x^2-5x^2+35)(x^2-35) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^4-12x^2+35)(x^2-35) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^6-35x^4-12x^4+420x^2+35x^2-1225 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^6-47x^4+455x^2-1225\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-5}\right) $ by each term in $ \left( x^2-7\right) $. $$ \left( \color{blue}{x^2-5}\right) \cdot \left( x^2-7\right) = x^4-7x^2-5x^2+35 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-7x^2} \color{blue}{-5x^2} +35 = x^4 \color{blue}{-12x^2} +35 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^4-12x^2+35}\right) $ by each term in $ \left( x^2-35\right) $. $$ \left( \color{blue}{x^4-12x^2+35}\right) \cdot \left( x^2-35\right) = x^6-35x^4-12x^4+420x^2+35x^2-1225 $$ |
| ④ | Combine like terms: $$ x^6 \color{blue}{-35x^4} \color{blue}{-12x^4} + \color{red}{420x^2} + \color{red}{35x^2} -1225 = x^6 \color{blue}{-47x^4} + \color{red}{455x^2} -1225 $$ |
This page was created using
Simplify polynomials calculator