Answer
$$(x+5)(x-2)(2x-1)^2=4x^4+8x^3-51x^2+43x-10$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+5)(x-2)(2x-1)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x+5)(x-2)(4x^2-4x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-2x+5x-10)(4x^2-4x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(x^2+3x-10)(4x^2-4x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^4+8x^3-51x^2+43x-10\end{aligned} $$ | |
| ① | Find $ \left(2x-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(2x-1\right)^2 = \color{blue}{\left( 2x \right)^2} -2 \cdot 2x \cdot 1 + \color{red}{1^2} = 4x^2-4x+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x+5}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x+5}\right) \cdot \left( x-2\right) = x^2-2x+5x-10 $$ |
| ③ | Combine like terms: $$ x^2 \color{blue}{-2x} + \color{blue}{5x} -10 = x^2+ \color{blue}{3x} -10 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{x^2+3x-10}\right) $ by each term in $ \left( 4x^2-4x+1\right) $. $$ \left( \color{blue}{x^2+3x-10}\right) \cdot \left( 4x^2-4x+1\right) = 4x^4-4x^3+x^2+12x^3-12x^2+3x-40x^2+40x-10 $$ |
| ⑤ | Combine like terms: $$ 4x^4 \color{blue}{-4x^3} + \color{red}{x^2} + \color{blue}{12x^3} \color{green}{-12x^2} + \color{orange}{3x} \color{green}{-40x^2} + \color{orange}{40x} -10 = \\ = 4x^4+ \color{blue}{8x^3} \color{green}{-51x^2} + \color{orange}{43x} -10 $$ |
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