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