Question
Answer
$$(5t-32)^2+(9t-54)^2+(3t-17)^2=115t^2-1394t+4229$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(5t-32)^2+(9t-54)^2+(3t-17)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}25t^2-320t+1024+81t^2-972t+2916+9t^2-102t+289 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}106t^2-1292t+3940+9t^2-102t+289 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}115t^2-1394t+4229\end{aligned} $$ | |
| ① | Find $ \left(5t-32\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 5t } $ and $ B = \color{red}{ 32 }$. $$ \begin{aligned}\left(5t-32\right)^2 = \color{blue}{\left( 5t \right)^2} -2 \cdot 5t \cdot 32 + \color{red}{32^2} = 25t^2-320t+1024\end{aligned} $$Find $ \left(9t-54\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 9t } $ and $ B = \color{red}{ 54 }$. $$ \begin{aligned}\left(9t-54\right)^2 = \color{blue}{\left( 9t \right)^2} -2 \cdot 9t \cdot 54 + \color{red}{54^2} = 81t^2-972t+2916\end{aligned} $$Find $ \left(3t-17\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3t } $ and $ B = \color{red}{ 17 }$. $$ \begin{aligned}\left(3t-17\right)^2 = \color{blue}{\left( 3t \right)^2} -2 \cdot 3t \cdot 17 + \color{red}{17^2} = 9t^2-102t+289\end{aligned} $$ |
| ② | Combine like terms: $$ \color{blue}{25t^2} \color{red}{-320t} + \color{green}{1024} + \color{blue}{81t^2} \color{red}{-972t} + \color{green}{2916} = \color{blue}{106t^2} \color{red}{-1292t} + \color{green}{3940} $$ |
| ③ | Combine like terms: $$ \color{blue}{106t^2} \color{red}{-1292t} + \color{green}{3940} + \color{blue}{9t^2} \color{red}{-102t} + \color{green}{289} = \color{blue}{115t^2} \color{red}{-1394t} + \color{green}{4229} $$ |
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