Question
Answer
$$2(x-2)^2(x+4)=2x^3-24x+32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-2)^2(x+4)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2-4x+4)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-8x+8)(x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+8x^2-8x^2-32x+8x+32 \xlongequal{ } \\[1 em] & \xlongequal{ }2x^3+ \cancel{8x^2} -\cancel{8x^2}-32x+8x+32 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-24x+32\end{aligned} $$ | |
| 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 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2-4x+4\right) $ $$ \color{blue}{2} \cdot \left( x^2-4x+4\right) = 2x^2-8x+8 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-8x+8}\right) $ by each term in $ \left( x+4\right) $. $$ \left( \color{blue}{2x^2-8x+8}\right) \cdot \left( x+4\right) = 2x^3+ \cancel{8x^2} -\cancel{8x^2}-32x+8x+32 $$ |
| ④ | Combine like terms: $$ 2x^3+ \, \color{blue}{ \cancel{8x^2}} \, \, \color{blue}{ -\cancel{8x^2}} \, \color{green}{-32x} + \color{green}{8x} +32 = 2x^3 \color{green}{-24x} +32 $$ |
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