Question
Answer
$$3a^3(2a-5b)-4a^3(2a+3b)=-2a^4-27a^3b$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3a^3(2a-5b)-4a^3(2a+3b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6a^4-15a^3b-(8a^4+12a^3b) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6a^4-15a^3b-8a^4-12a^3b \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-2a^4-27a^3b\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{3a^3} $ by $ \left( 2a-5b\right) $ $$ \color{blue}{3a^3} \cdot \left( 2a-5b\right) = 6a^4-15a^3b $$Multiply $ \color{blue}{4a^3} $ by $ \left( 2a+3b\right) $ $$ \color{blue}{4a^3} \cdot \left( 2a+3b\right) = 8a^4+12a^3b $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 8a^4+12a^3b \right) = -8a^4-12a^3b $$ |
| ③ | Combine like terms: $$ \color{blue}{6a^4} \color{red}{-15a^3b} \color{blue}{-8a^4} \color{red}{-12a^3b} = \color{blue}{-2a^4} \color{red}{-27a^3b} $$ |
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