Question
Answer
$$2x(x-5)(x+2)-(3x-2)^2=2x^3-15x^2-8x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2x(x-5)(x+2)-(3x-2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2x(x-5)(x+2)-(9x^2-12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(2x^2-10x)(x+2)-(9x^2-12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^3+4x^2-10x^2-20x-(9x^2-12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^3-6x^2-20x-(9x^2-12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}2x^3-6x^2-20x-9x^2+12x-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2x^3-15x^2-8x-4\end{aligned} $$ | |
| ① | Find $ \left(3x-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}{ 3x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(3x-2\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2-12x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2x} $ by $ \left( x-5\right) $ $$ \color{blue}{2x} \cdot \left( x-5\right) = 2x^2-10x $$ |
| ③ | Multiply each term of $ \left( \color{blue}{2x^2-10x}\right) $ by each term in $ \left( x+2\right) $. $$ \left( \color{blue}{2x^2-10x}\right) \cdot \left( x+2\right) = 2x^3+4x^2-10x^2-20x $$ |
| ④ | Combine like terms: $$ 2x^3+ \color{blue}{4x^2} \color{blue}{-10x^2} -20x = 2x^3 \color{blue}{-6x^2} -20x $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9x^2-12x+4 \right) = -9x^2+12x-4 $$ |
| ⑥ | Combine like terms: $$ 2x^3 \color{blue}{-6x^2} \color{red}{-20x} \color{blue}{-9x^2} + \color{red}{12x} -4 = 2x^3 \color{blue}{-15x^2} \color{red}{-8x} -4 $$ |
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