Question
Answer
$$3(x+5)^2+2(x+5)-5=3x^2+32x+80$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}3(x+5)^2+2(x+5)-5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3(x^2+10x+25)+2(x+5)-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^2+30x+75+2x+10-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^2+32x+85-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^2+32x+80\end{aligned} $$ | |
| 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}{2} $ by $ \left( x+5\right) $ $$ \color{blue}{2} \cdot \left( x+5\right) = 2x+10 $$ |
| ③ | Combine like terms: $$ 3x^2+ \color{blue}{30x} + \color{red}{75} + \color{blue}{2x} + \color{red}{10} = 3x^2+ \color{blue}{32x} + \color{red}{85} $$ |
| ④ | Combine like terms: $$ 3x^2+32x+ \color{blue}{85} \color{blue}{-5} = 3x^2+32x+ \color{blue}{80} $$ |
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