Answer
$$6y^2-2(3y+2)(y-1)-(y-2)(2y+1)=-2y^2+5y+6$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6y^2-2(3y+2)(y-1)-(y-2)(2y+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6y^2-(6y+4)(y-1)-(2y^2+y-4y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6y^2-(6y+4)(y-1)-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}6y^2-(6y^2-6y+4y-4)-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}6y^2-(6y^2-2y-4)-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}6y^2-6y^2+2y+4-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}2y+4-(2y^2-3y-2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}2y+4-2y^2+3y+2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-2y^2+5y+6\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{2} $ by $ \left( 3y+2\right) $ $$ \color{blue}{2} \cdot \left( 3y+2\right) = 6y+4 $$ 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}{6y+4}\right) $ by each term in $ \left( y-1\right) $. $$ \left( \color{blue}{6y+4}\right) \cdot \left( y-1\right) = 6y^2-6y+4y-4 $$ |
| ④ | Combine like terms: $$ 6y^2 \color{blue}{-6y} + \color{blue}{4y} -4 = 6y^2 \color{blue}{-2y} -4 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 6y^2-2y-4 \right) = -6y^2+2y+4 $$ |
| ⑥ | Combine like terms: $$ \, \color{blue}{ \cancel{6y^2}} \, \, \color{blue}{ -\cancel{6y^2}} \,+2y+4 = 2y+4 $$ |
| ⑦ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2y^2-3y-2 \right) = -2y^2+3y+2 $$ |
| ⑧ | Combine like terms: $$ \color{blue}{2y} + \color{red}{4} -2y^2+ \color{blue}{3y} + \color{red}{2} = -2y^2+ \color{blue}{5y} + \color{red}{6} $$ |
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