Question
Answer
$$(2a-3b)(a^2-ab+3b)=2a^3-5a^2b+3ab^2+6ab-9b^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2a-3b)(a^2-ab+3b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2a^3-2a^2b+6ab-3a^2b+3ab^2-9b^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2a^3-5a^2b+3ab^2+6ab-9b^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2a-3b}\right) $ by each term in $ \left( a^2-ab+3b\right) $. $$ \left( \color{blue}{2a-3b}\right) \cdot \left( a^2-ab+3b\right) = 2a^3-2a^2b+6ab-3a^2b+3ab^2-9b^2 $$ |
| ② | Combine like terms: $$ 2a^3 \color{blue}{-2a^2b} +6ab \color{blue}{-3a^2b} +3ab^2-9b^2 = 2a^3 \color{blue}{-5a^2b} +3ab^2+6ab-9b^2 $$ |
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