Question
Answer
$$(9-4x)^2+(10-4x)^2+(9-2x)^2+(12-6x)^2+(13-8x)^2=136x^2-540x+575$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(9-4x)^2+(10-4x)^2+(9-2x)^2+(12-6x)^2+(13-8x)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}81-72x+16x^2+100-80x+16x^2+81-36x+4x^2+144-144x+36x^2+169-208x+64x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}32x^2-152x+181+81-36x+4x^2+144-144x+36x^2+169-208x+64x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}36x^2-188x+262+144-144x+36x^2+169-208x+64x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}72x^2-332x+406+169-208x+64x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}136x^2-540x+575\end{aligned} $$ | |
| ① | Find $ \left(9-4x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 9 } $ and $ B = \color{red}{ 4x }$. $$ \begin{aligned}\left(9-4x\right)^2 = \color{blue}{9^2} -2 \cdot 9 \cdot 4x + \color{red}{\left( 4x \right)^2} = 81-72x+16x^2\end{aligned} $$Find $ \left(10-4x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 10 } $ and $ B = \color{red}{ 4x }$. $$ \begin{aligned}\left(10-4x\right)^2 = \color{blue}{10^2} -2 \cdot 10 \cdot 4x + \color{red}{\left( 4x \right)^2} = 100-80x+16x^2\end{aligned} $$Find $ \left(9-2x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 9 } $ and $ B = \color{red}{ 2x }$. $$ \begin{aligned}\left(9-2x\right)^2 = \color{blue}{9^2} -2 \cdot 9 \cdot 2x + \color{red}{\left( 2x \right)^2} = 81-36x+4x^2\end{aligned} $$Find $ \left(12-6x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 12 } $ and $ B = \color{red}{ 6x }$. $$ \begin{aligned}\left(12-6x\right)^2 = \color{blue}{12^2} -2 \cdot 12 \cdot 6x + \color{red}{\left( 6x \right)^2} = 144-144x+36x^2\end{aligned} $$Find $ \left(13-8x\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 13 } $ and $ B = \color{red}{ 8x }$. $$ \begin{aligned}\left(13-8x\right)^2 = \color{blue}{13^2} -2 \cdot 13 \cdot 8x + \color{red}{\left( 8x \right)^2} = 169-208x+64x^2\end{aligned} $$ |
| ② | Combine like terms: $$ \color{blue}{81} \color{red}{-72x} + \color{green}{16x^2} + \color{blue}{100} \color{red}{-80x} + \color{green}{16x^2} = \color{green}{32x^2} \color{red}{-152x} + \color{blue}{181} $$ |
| ③ | Combine like terms: $$ \color{blue}{32x^2} \color{red}{-152x} + \color{green}{181} + \color{green}{81} \color{red}{-36x} + \color{blue}{4x^2} = \color{blue}{36x^2} \color{red}{-188x} + \color{green}{262} $$ |
| ④ | Combine like terms: $$ \color{blue}{36x^2} \color{red}{-188x} + \color{green}{262} + \color{green}{144} \color{red}{-144x} + \color{blue}{36x^2} = \color{blue}{72x^2} \color{red}{-332x} + \color{green}{406} $$ |
| ⑤ | Combine like terms: $$ \color{blue}{72x^2} \color{red}{-332x} + \color{green}{406} + \color{green}{169} \color{red}{-208x} + \color{blue}{64x^2} = \color{blue}{136x^2} \color{red}{-540x} + \color{green}{575} $$ |
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