Question
Answer
$$(2x-1)^2+3(2x-1)-5=4x^2+2x-7$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x-1)^2+3(2x-1)-5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2-4x+1+3(2x-1)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2-4x+1+6x-3-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+2x-2-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2+2x-7\end{aligned} $$ | |
| ① | Find $ \left(2x-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}{ 2x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(2x-1\right)^2 = \color{blue}{\left( 2x \right)^2} -2 \cdot 2x \cdot 1 + \color{red}{1^2} = 4x^2-4x+1\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( 2x-1\right) $ $$ \color{blue}{3} \cdot \left( 2x-1\right) = 6x-3 $$ |
| ③ | Combine like terms: $$ 4x^2 \color{blue}{-4x} + \color{red}{1} + \color{blue}{6x} \color{red}{-3} = 4x^2+ \color{blue}{2x} \color{red}{-2} $$ |
| ④ | Combine like terms: $$ 4x^2+2x \color{blue}{-2} \color{blue}{-5} = 4x^2+2x \color{blue}{-7} $$ |
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