Answer
$$(x+6y)(6x^2-xy-2y^2)=6x^3+35x^2y-8xy^2-12y^3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+6y)(6x^2-xy-2y^2)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6x^3-x^2y-2xy^2+36x^2y-6xy^2-12y^3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6x^3+35x^2y-8xy^2-12y^3\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x+6y}\right) $ by each term in $ \left( 6x^2-xy-2y^2\right) $. $$ \left( \color{blue}{x+6y}\right) \cdot \left( 6x^2-xy-2y^2\right) = 6x^3-x^2y-2xy^2+36x^2y-6xy^2-12y^3 $$ |
| ② | Combine like terms: $$ 6x^3 \color{blue}{-x^2y} \color{red}{-2xy^2} + \color{blue}{36x^2y} \color{red}{-6xy^2} -12y^3 = 6x^3+ \color{blue}{35x^2y} \color{red}{-8xy^2} -12y^3 $$ |
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