Question
Answer
$$(x-2)(x+2)(x^2+4)=x^4-16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x+2)(x^2+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x-2x-4)(x^2+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-4)(x^2+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^4+4x^2-4x^2-16 \xlongequal{ } \\[1 em] & \xlongequal{ }x^4+ \cancel{4x^2} -\cancel{4x^2}-16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^4-16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x+2\right) = x^2+ \cancel{2x} -\cancel{2x}-4 $$ |
| ② | Combine like terms: $$ x^2+ \, \color{blue}{ \cancel{2x}} \, \, \color{blue}{ -\cancel{2x}} \,-4 = x^2-4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-4}\right) $ by each term in $ \left( x^2+4\right) $. $$ \left( \color{blue}{x^2-4}\right) \cdot \left( x^2+4\right) = x^4+ \cancel{4x^2} -\cancel{4x^2}-16 $$ |
| ④ | Combine like terms: $$ x^4+ \, \color{blue}{ \cancel{4x^2}} \, \, \color{blue}{ -\cancel{4x^2}} \,-16 = x^4-16 $$ |
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