Question
Answer
$$(7-y^8)\cdot(7+y^8)=-y^{16}+49$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(7-y^8)\cdot(7+y^8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}49+7y^8-7y^8-y^{16} \xlongequal{ } \\[1 em] & \xlongequal{ }49+ \cancel{7y^8} -\cancel{7y^8}-y^{16} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-y^{16}+49\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{7-y^8}\right) $ by each term in $ \left( 7+y^8\right) $. $$ \left( \color{blue}{7-y^8}\right) \cdot \left( 7+y^8\right) = 49+ \cancel{7y^8} -\cancel{7y^8}-y^{16} $$ |
| ② | Combine like terms: $$ 49+ \, \color{blue}{ \cancel{7y^8}} \, \, \color{blue}{ -\cancel{7y^8}} \,-y^{16} = -y^{16}+49 $$ |
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