Question
Answer
$$(2a^3+5b)(-2a^3+3ab^2-7b)=-4a^6+6a^4b^2-24a^3b+15ab^3-35b^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2a^3+5b)(-2a^3+3ab^2-7b)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}-4a^6+6a^4b^2-14a^3b-10a^3b+15ab^3-35b^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}-4a^6+6a^4b^2-24a^3b+15ab^3-35b^2\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{2a^3+5b}\right) $ by each term in $ \left( -2a^3+3ab^2-7b\right) $. $$ \left( \color{blue}{2a^3+5b}\right) \cdot \left( -2a^3+3ab^2-7b\right) = -4a^6+6a^4b^2-14a^3b-10a^3b+15ab^3-35b^2 $$ |
| ② | Combine like terms: $$ -4a^6+6a^4b^2 \color{blue}{-14a^3b} \color{blue}{-10a^3b} +15ab^3-35b^2 = -4a^6+6a^4b^2 \color{blue}{-24a^3b} +15ab^3-35b^2 $$ |
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