Question
Answer
$$(x^2+2x-(x-2)^2)(x^2-2x-(x+2)^2)=-36x^2+16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x^2+2x-(x-2)^2)(x^2-2x-(x+2)^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2+2x-(x^2-4x+4))(x^2-2x-(x^2+4x+4)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2+2x-x^2+4x-4)(x^2-2x-x^2-4x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(6x-4)(-6x-4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-36x^2-24x+24x+16 \xlongequal{ } \\[1 em] & \xlongequal{ }-36x^2 -\cancel{24x}+ \cancel{24x}+16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-36x^2+16\end{aligned} $$ | |
| ① | Find $ \left(x-2\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$Find $ \left(x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(x+2\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 2 + \color{red}{2^2} = x^2+4x+4\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-4x+4 \right) = -x^2+4x-4 $$Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+4x+4 \right) = -x^2-4x-4 $$ |
| ③ | Combine like terms: $$ \, \color{blue}{ \cancel{x^2}} \,+ \color{green}{2x} \, \color{blue}{ -\cancel{x^2}} \,+ \color{green}{4x} -4 = \color{green}{6x} -4 $$Combine like terms: $$ \, \color{blue}{ \cancel{x^2}} \, \color{green}{-2x} \, \color{blue}{ -\cancel{x^2}} \, \color{green}{-4x} -4 = \color{green}{-6x} -4 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{6x-4}\right) $ by each term in $ \left( -6x-4\right) $. $$ \left( \color{blue}{6x-4}\right) \cdot \left( -6x-4\right) = -36x^2 -\cancel{24x}+ \cancel{24x}+16 $$ |
| ⑤ | Combine like terms: $$ -36x^2 \, \color{blue}{ -\cancel{24x}} \,+ \, \color{blue}{ \cancel{24x}} \,+16 = -36x^2+16 $$ |
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