Question
Answer
$$(x-20)(-22.325x^2+4741.65x+127476)-(x-50)(43.9x^2+134.6x+206454)=-65x^3+7197x^2-167098x+7773180$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-20)(-22.325x^2+4741.65x+127476)-(x-50)(43.9x^2+134.6x+206454)& \xlongequal{ }(x-20)(-22x^2+4741x+127476)-(x-50)(43x^2+134x+206454) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-22x^3+4741x^2+127476x+440x^2-94820x-2549520-(43x^3+134x^2+206454x-2150x^2-6700x-10322700) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-22x^3+5181x^2+32656x-2549520-(43x^3-2016x^2+199754x-10322700) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-22x^3+5181x^2+32656x-2549520-43x^3+2016x^2-199754x+10322700 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-65x^3+7197x^2-167098x+7773180\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-20}\right) $ by each term in $ \left( -22x^2+4741x+127476\right) $. $$ \left( \color{blue}{x-20}\right) \cdot \left( -22x^2+4741x+127476\right) = -22x^3+4741x^2+127476x+440x^2-94820x-2549520 $$Multiply each term of $ \left( \color{blue}{x-50}\right) $ by each term in $ \left( 43x^2+134x+206454\right) $. $$ \left( \color{blue}{x-50}\right) \cdot \left( 43x^2+134x+206454\right) = 43x^3+134x^2+206454x-2150x^2-6700x-10322700 $$ |
| ② | Combine like terms: $$ -22x^3+ \color{blue}{4741x^2} + \color{red}{127476x} + \color{blue}{440x^2} \color{red}{-94820x} -2549520 = -22x^3+ \color{blue}{5181x^2} + \color{red}{32656x} -2549520 $$Combine like terms: $$ 43x^3+ \color{blue}{134x^2} + \color{red}{206454x} \color{blue}{-2150x^2} \color{red}{-6700x} -10322700 = 43x^3 \color{blue}{-2016x^2} + \color{red}{199754x} -10322700 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 43x^3-2016x^2+199754x-10322700 \right) = -43x^3+2016x^2-199754x+10322700 $$ |
| ④ | Combine like terms: $$ \color{blue}{-22x^3} + \color{red}{5181x^2} + \color{green}{32656x} \color{orange}{-2549520} \color{blue}{-43x^3} + \color{red}{2016x^2} \color{green}{-199754x} + \color{orange}{10322700} = \\ = \color{blue}{-65x^3} + \color{red}{7197x^2} \color{green}{-167098x} + \color{orange}{7773180} $$ |
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