Question
Answer
$$9x^2-7x-(3x+5)^2=-37x-25$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}9x^2-7x-(3x+5)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2-7x-(9x^2+30x+25) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2-7x-9x^2-30x-25 \xlongequal{ } \\[1 em] & \xlongequal{ } \cancel{9x^2}-7x -\cancel{9x^2}-30x-25 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-37x-25\end{aligned} $$ | |
| 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: $$ \, \color{blue}{ \cancel{9x^2}} \, \color{green}{-7x} \, \color{blue}{ -\cancel{9x^2}} \, \color{green}{-30x} -25 = \color{green}{-37x} -25 $$ |
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