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