Answer
$$(p^2+p-6)(p^2-6)=p^4+p^3-12p^2-6p+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(p^2+p-6)(p^2-6)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}p^4-6p^2+p^3-6p-6p^2+36 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}p^4+p^3-12p^2-6p+36\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{p^2+p-6}\right) $ by each term in $ \left( p^2-6\right) $. $$ \left( \color{blue}{p^2+p-6}\right) \cdot \left( p^2-6\right) = p^4-6p^2+p^3-6p-6p^2+36 $$ |
| ② | Combine like terms: $$ p^4 \color{blue}{-6p^2} +p^3-6p \color{blue}{-6p^2} +36 = p^4+p^3 \color{blue}{-12p^2} -6p+36 $$ |
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