Question
Answer
$$-(x-1)^3(4x-1)^2=-16x^5+56x^4-73x^3+43x^2-11x+1$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x-1)^3(4x-1)^2& \xlongequal{ }-(x^3-3x^2+3x-1)(16x^2-8x+1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(16x^5-56x^4+73x^3-43x^2+11x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-16x^5+56x^4-73x^3+43x^2-11x+1\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^3-3x^2+3x-1}\right) $ by each term in $ \left( 16x^2-8x+1\right) $. $$ \left( \color{blue}{x^3-3x^2+3x-1}\right) \cdot \left( 16x^2-8x+1\right) = \\ = 16x^5-8x^4+x^3-48x^4+24x^3-3x^2+48x^3-24x^2+3x-16x^2+8x-1 $$ |
| ② | Combine like terms: $$ 16x^5 \color{blue}{-8x^4} + \color{red}{x^3} \color{blue}{-48x^4} + \color{green}{24x^3} \color{orange}{-3x^2} + \color{green}{48x^3} \color{blue}{-24x^2} + \color{red}{3x} \color{blue}{-16x^2} + \color{red}{8x} -1 = \\ = 16x^5 \color{blue}{-56x^4} + \color{green}{73x^3} \color{blue}{-43x^2} + \color{red}{11x} -1 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(16x^5-56x^4+73x^3-43x^2+11x-1 \right) = -16x^5+56x^4-73x^3+43x^2-11x+1 $$ |
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