Question
Answer
$$2(x-4)^2+3(x-4)+1=2x^2-13x+21$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x-4)^2+3(x-4)+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2-8x+16)+3(x-4)+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2-16x+32+3x-12+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2-13x+20+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2-13x+21\end{aligned} $$ | |
| ① | Find $ \left(x-4\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 4 }$. $$ \begin{aligned}\left(x-4\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 4 + \color{red}{4^2} = x^2-8x+16\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x^2-8x+16\right) $ $$ \color{blue}{2} \cdot \left( x^2-8x+16\right) = 2x^2-16x+32 $$Multiply $ \color{blue}{3} $ by $ \left( x-4\right) $ $$ \color{blue}{3} \cdot \left( x-4\right) = 3x-12 $$ |
| ③ | Combine like terms: $$ 2x^2 \color{blue}{-16x} + \color{red}{32} + \color{blue}{3x} \color{red}{-12} = 2x^2 \color{blue}{-13x} + \color{red}{20} $$ |
| ④ | Combine like terms: $$ 2x^2-13x+ \color{blue}{20} + \color{blue}{1} = 2x^2-13x+ \color{blue}{21} $$ |
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