Question
Answer
$$2(3x-1)^2+5x^2-x+1=23x^2-13x+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(3x-1)^2+5x^2-x+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(9x^2-6x+1)+5x^2-x+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}18x^2-12x+2+5x^2-x+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}23x^2-13x+3\end{aligned} $$ | |
| ① | Find $ \left(3x-1\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}{ 1 }$. $$ \begin{aligned}\left(3x-1\right)^2 = \color{blue}{\left( 3x \right)^2} -2 \cdot 3x \cdot 1 + \color{red}{1^2} = 9x^2-6x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( 9x^2-6x+1\right) $ $$ \color{blue}{2} \cdot \left( 9x^2-6x+1\right) = 18x^2-12x+2 $$ |
| ③ | Combine like terms: $$ \color{blue}{18x^2} \color{red}{-12x} + \color{green}{2} + \color{blue}{5x^2} \color{red}{-x} + \color{green}{1} = \color{blue}{23x^2} \color{red}{-13x} + \color{green}{3} $$ |
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