Question
Answer
$$-(x+5)^2(x-4)^2=-x^4-2x^3+39x^2+40x-400$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}-(x+5)^2(x-4)^2& \xlongequal{ }-(x^2+10x+25)(x^2-8x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-(x^4+2x^3-39x^2-40x+400) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-x^4-2x^3+39x^2+40x-400\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x^2+10x+25}\right) $ by each term in $ \left( x^2-8x+16\right) $. $$ \left( \color{blue}{x^2+10x+25}\right) \cdot \left( x^2-8x+16\right) = x^4-8x^3+16x^2+10x^3-80x^2+160x+25x^2-200x+400 $$ |
| ② | Combine like terms: $$ x^4 \color{blue}{-8x^3} + \color{red}{16x^2} + \color{blue}{10x^3} \color{green}{-80x^2} + \color{orange}{160x} + \color{green}{25x^2} \color{orange}{-200x} +400 = \\ = x^4+ \color{blue}{2x^3} \color{green}{-39x^2} \color{orange}{-40x} +400 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left(x^4+2x^3-39x^2-40x+400 \right) = -x^4-2x^3+39x^2+40x-400 $$ |
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