Question
Answer
$$(3x-6)^2-7(3x-6)+3=9x^2-57x+81$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(3x-6)^2-7(3x-6)+3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}9x^2-36x+36-7(3x-6)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}9x^2-36x+36-(21x-42)+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}9x^2-36x+36-21x+42+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}9x^2-57x+81\end{aligned} $$ | |
| ① | Find $ \left(3x-6\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}{ 6 }$. $$ \begin{aligned}\left(3x-6\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 6 + \color{red}{6^2} = 9x^2-36x+36\end{aligned} $$ |
| ② | Multiply $ \color{blue}{7} $ by $ \left( 3x-6\right) $ $$ \color{blue}{7} \cdot \left( 3x-6\right) = 21x-42 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 21x-42 \right) = -21x+42 $$ |
| ④ | Combine like terms: $$ 9x^2 \color{blue}{-36x} + \color{red}{36} \color{blue}{-21x} + \color{green}{42} + \color{green}{3} = 9x^2 \color{blue}{-57x} + \color{green}{81} $$ |
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