Question
Answer
$$(r^3+r^2)^2-4r^3(r^2+r)=r^6-2r^5-3r^4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(r^3+r^2)^2-4r^3(r^2+r)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}r^6+2r^5+r^4-4r^3(r^2+r) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}r^6+2r^5+r^4-(4r^5+4r^4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}r^6+2r^5+r^4-4r^5-4r^4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}r^6-2r^5-3r^4\end{aligned} $$ | |
| ① | Find $ \left(r^3+r^2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ r^3 } $ and $ B = \color{red}{ r^2 }$. $$ \begin{aligned}\left(r^3+r^2\right)^2 = \color{blue}{\left( r^3 \right)^2} +2 \cdot r^3 \cdot r^2 + \color{red}{\left( r^2 \right)^2} = r^6+2r^5+r^4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4r^3} $ by $ \left( r^2+r\right) $ $$ \color{blue}{4r^3} \cdot \left( r^2+r\right) = 4r^5+4r^4 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 4r^5+4r^4 \right) = -4r^5-4r^4 $$ |
| ④ | Combine like terms: $$ r^6+ \color{blue}{2r^5} + \color{red}{r^4} \color{blue}{-4r^5} \color{red}{-4r^4} = r^6 \color{blue}{-2r^5} \color{red}{-3r^4} $$ |
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