Question
Answer
$$3(x-5)^2+5(x-5)-2=3x^2-25x+48$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x-5)^2+5(x-5)-2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(x^2-10x+25)+5(x-5)-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2-30x+75+5x-25-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2-25x+50-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^2-25x+48\end{aligned} $$ | |
| ① | Find $ \left(x-5\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}{ 5 }$. $$ \begin{aligned}\left(x-5\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 5 + \color{red}{5^2} = x^2-10x+25\end{aligned} $$ |
| ② | Multiply $ \color{blue}{3} $ by $ \left( x^2-10x+25\right) $ $$ \color{blue}{3} \cdot \left( x^2-10x+25\right) = 3x^2-30x+75 $$Multiply $ \color{blue}{5} $ by $ \left( x-5\right) $ $$ \color{blue}{5} \cdot \left( x-5\right) = 5x-25 $$ |
| ③ | Combine like terms: $$ 3x^2 \color{blue}{-30x} + \color{red}{75} + \color{blue}{5x} \color{red}{-25} = 3x^2 \color{blue}{-25x} + \color{red}{50} $$ |
| ④ | Combine like terms: $$ 3x^2-25x+ \color{blue}{50} \color{blue}{-2} = 3x^2-25x+ \color{blue}{48} $$ |
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