Question
Answer
$$9x^2+2x+8-(x-4)^2=8x^2+10x-8$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9x^2+2x+8-(x-4)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2+2x+8-(x^2-8x+16) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2+2x+8-x^2+8x-16 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}8x^2+10x-8\end{aligned} $$ | |
| ① | Find $ \left(x-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}{ x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(x-4\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 4 + \color{red}{4^2} = x^2-8x+16\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-8x+16 \right) = -x^2+8x-16 $$ |
| ③ | Combine like terms: $$ \color{blue}{9x^2} + \color{red}{2x} + \color{green}{8} \color{blue}{-x^2} + \color{red}{8x} \color{green}{-16} = \color{blue}{8x^2} + \color{red}{10x} \color{green}{-8} $$ |
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