Question
Answer
$$(24+11k)\cdot(40+30k)-(k+2)\cdot20k=310k^2+1120k+960$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(24+11k)\cdot(40+30k)-(k+2)\cdot20k& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}960+720k+440k+330k^2-(20k^2+40k) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}330k^2+1160k+960-(20k^2+40k) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}330k^2+1160k+960-20k^2-40k \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}310k^2+1120k+960\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{24+11k}\right) $ by each term in $ \left( 40+30k\right) $. $$ \left( \color{blue}{24+11k}\right) \cdot \left( 40+30k\right) = 960+720k+440k+330k^2 $$$$ \left( \color{blue}{k+2}\right) \cdot 20k = 20k^2+40k $$ |
| ② | Combine like terms: $$ 960+ \color{blue}{720k} + \color{blue}{440k} +330k^2 = 330k^2+ \color{blue}{1160k} +960 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 20k^2+40k \right) = -20k^2-40k $$ |
| ④ | Combine like terms: $$ \color{blue}{330k^2} + \color{red}{1160k} +960 \color{blue}{-20k^2} \color{red}{-40k} = \color{blue}{310k^2} + \color{red}{1120k} +960 $$ |
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