Question
Answer
$$(y+4)^3-2y(y-1)=y^3+10y^2+50y+64$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(y+4)^3-2y(y-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}y^3+12y^2+48y+64-2y(y-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}y^3+12y^2+48y+64-(2y^2-2y) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}y^3+12y^2+48y+64-2y^2+2y \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}y^3+10y^2+50y+64\end{aligned} $$ | |
| ① | Find $ \left(y+4\right)^3 $ using formula $$ (A + B) = A^3 + 3A^2B + 3AB^2 + B^3 $$where $ A = y $ and $ B = 4 $. $$ \left(y+4\right)^3 = y^3+3 \cdot y^2 \cdot 4 + 3 \cdot y \cdot 4^2+4^3 = y^3+12y^2+48y+64 $$ |
| ② | Multiply $ \color{blue}{2y} $ by $ \left( y-1\right) $ $$ \color{blue}{2y} \cdot \left( y-1\right) = 2y^2-2y $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2y^2-2y \right) = -2y^2+2y $$ |
| ④ | Combine like terms: $$ y^3+ \color{blue}{12y^2} + \color{red}{48y} +64 \color{blue}{-2y^2} + \color{red}{2y} = y^3+ \color{blue}{10y^2} + \color{red}{50y} +64 $$ |
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