Answer
$$6y^2(3y+2)(y-1)-(y-2)(2y+1)=18y^4-6y^3-14y^2+3y+2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6y^2(3y+2)(y-1)-(y-2)(2y+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(18y^3+12y^2)(y-1)-(2y^2+y-4y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(18y^3+12y^2)(y-1)-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}18y^4-18y^3+12y^3-12y^2-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}18y^4-6y^3-12y^2-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}18y^4-6y^3-12y^2-2y^2+3y+2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}18y^4-6y^3-14y^2+3y+2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{6y^2} $ by $ \left( 3y+2\right) $ $$ \color{blue}{6y^2} \cdot \left( 3y+2\right) = 18y^3+12y^2 $$ Multiply each term of $ \left( \color{blue}{y-2}\right) $ by each term in $ \left( 2y+1\right) $. $$ \left( \color{blue}{y-2}\right) \cdot \left( 2y+1\right) = 2y^2+y-4y-2 $$ |
| ② | Combine like terms: $$ 2y^2+ \color{blue}{y} \color{blue}{-4y} -2 = 2y^2 \color{blue}{-3y} -2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{18y^3+12y^2}\right) $ by each term in $ \left( y-1\right) $. $$ \left( \color{blue}{18y^3+12y^2}\right) \cdot \left( y-1\right) = 18y^4-18y^3+12y^3-12y^2 $$ |
| ④ | Combine like terms: $$ 18y^4 \color{blue}{-18y^3} + \color{blue}{12y^3} -12y^2 = 18y^4 \color{blue}{-6y^3} -12y^2 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2y^2-3y-2 \right) = -2y^2+3y+2 $$ |
| ⑥ | Combine like terms: $$ 18y^4-6y^3 \color{blue}{-12y^2} \color{blue}{-2y^2} +3y+2 = 18y^4-6y^3 \color{blue}{-14y^2} +3y+2 $$ |
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