Question
Answer
$$-(x-1)^2(x-4)^2=-x^4+10x^3-33x^2+40x-16$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x-1)^2(x-4)^2& \xlongequal{ }-(x^2-2x+1)(x^2-8x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(x^4-10x^3+33x^2-40x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^4+10x^3-33x^2+40x-16\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2-2x+1}\right) $ by each term in $ \left( x^2-8x+16\right) $. $$ \left( \color{blue}{x^2-2x+1}\right) \cdot \left( x^2-8x+16\right) = x^4-8x^3+16x^2-2x^3+16x^2-32x+x^2-8x+16 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-8x^3} + \color{red}{16x^2} \color{blue}{-2x^3} + \color{green}{16x^2} \color{orange}{-32x} + \color{green}{x^2} \color{orange}{-8x} +16 = \\ = x^4 \color{blue}{-10x^3} + \color{green}{33x^2} \color{orange}{-40x} +16 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(x^4-10x^3+33x^2-40x+16 \right) = -x^4+10x^3-33x^2+40x-16 $$ |
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