Question
Answer
$$(x+4)^2-2(x+4)+5=x^2+6x+13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x+4)^2-2(x+4)+5& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2+8x+16-2(x+4)+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^2+8x+16-(2x+8)+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^2+8x+16-2x-8+5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^2+6x+13\end{aligned} $$ | |
| ① | Find $ \left(x+4\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}{ 4 }$. $$ \begin{aligned}\left(x+4\right)^2 = \color{blue}{x^2} +2 \cdot x \cdot 4 + \color{red}{4^2} = x^2+8x+16\end{aligned} $$ |
| ② | Multiply $ \color{blue}{2} $ by $ \left( x+4\right) $ $$ \color{blue}{2} \cdot \left( x+4\right) = 2x+8 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 2x+8 \right) = -2x-8 $$ |
| ④ | Combine like terms: $$ x^2+ \color{blue}{8x} + \color{red}{16} \color{blue}{-2x} \color{green}{-8} + \color{green}{5} = x^2+ \color{blue}{6x} + \color{green}{13} $$ |
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