Answer
$$2(x+5)^2-3(x+5)+1=2x^2+17x+36$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}2(x+5)^2-3(x+5)+1& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}2(x^2+10x+25)-3(x+5)+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}2x^2+20x+50-(3x+15)+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}2x^2+20x+50-3x-15+1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}2x^2+17x+36\end{aligned} $$ | |
| 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}{2} $ by $ \left( x^2+10x+25\right) $ $$ \color{blue}{2} \cdot \left( x^2+10x+25\right) = 2x^2+20x+50 $$Multiply $ \color{blue}{3} $ by $ \left( x+5\right) $ $$ \color{blue}{3} \cdot \left( x+5\right) = 3x+15 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 3x+15 \right) = -3x-15 $$ |
| ④ | Combine like terms: $$ 2x^2+ \color{blue}{20x} + \color{red}{50} \color{blue}{-3x} \color{green}{-15} + \color{green}{1} = 2x^2+ \color{blue}{17x} + \color{green}{36} $$ |
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