Answer
$$6w^2-(w+4)^2+5w-9=5w^2-3w-25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}6w^2-(w+4)^2+5w-9& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}6w^2-(1w^2+8w+16)+5w-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}6w^2-w^2-8w-16+5w-9 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}5w^2-3w-25\end{aligned} $$ | |
| ① | Find $ \left(w+4\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ w } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(w+4\right)^2 = \color{blue}{w^2} +2 \cdot w \cdot 4 + \color{red}{4^2} = w^2+8w+16\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( w^2+8w+16 \right) = -w^2-8w-16 $$ |
| ③ | Combine like terms: $$ \color{blue}{6w^2} \color{blue}{-w^2} \color{red}{-8w} \color{green}{-16} + \color{red}{5w} \color{green}{-9} = \color{blue}{5w^2} \color{red}{-3w} \color{green}{-25} $$ |
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