Question
Answer
$$16-(3x-5)^2=-9x^2+30x-9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}16-(3x-5)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}16-(9x^2-30x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}16-9x^2+30x-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-9x^2+30x-9\end{aligned} $$ | |
| ① | Find $ \left(3x-5\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 5 }$. $$ \begin{aligned}\left(3x-5\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 5 + \color{red}{5^2} = 9x^2-30x+25\end{aligned} $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9x^2-30x+25 \right) = -9x^2+30x-25 $$ |
| ③ | Combine like terms: $$ \color{blue}{16} -9x^2+30x \color{blue}{-25} = -9x^2+30x \color{blue}{-9} $$ |
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