Question
Answer
$$(2x+3)^2+8(3-x-(x+2)(x-2))=-4x^2+4x+65$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(2x+3)^2+8(3-x-(x+2)(x-2))& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2+12x+9+8(3-x-(x+2)(x-2)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2+12x+9+8(3-x-(x^2-2x+2x-4)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+12x+9+8(3-x-(x^2-4)) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}4x^2+12x+9+8(3-x-x^2+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}4x^2+12x+9+8(-x^2-x+7) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}4x^2+12x+9-8x^2-8x+56 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-4x^2+4x+65\end{aligned} $$ | |
| ① | Find $ \left(2x+3\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 2x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(2x+3\right)^2 = \color{blue}{\left( 2x \right)^2} +2 \cdot 2x \cdot 3 + \color{red}{3^2} = 4x^2+12x+9\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x+2}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x+2}\right) \cdot \left( x-2\right) = x^2 -\cancel{2x}+ \cancel{2x}-4 $$ |
| ③ | Combine like terms: $$ x^2 \, \color{blue}{ -\cancel{2x}} \,+ \, \color{blue}{ \cancel{2x}} \,-4 = x^2-4 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-4 \right) = -x^2+4 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3} -x-x^2+ \color{blue}{4} = -x^2-x+ \color{blue}{7} $$ |
| ⑥ | Multiply $ \color{blue}{8} $ by $ \left( -x^2-x+7\right) $ $$ \color{blue}{8} \cdot \left( -x^2-x+7\right) = -8x^2-8x+56 $$ |
| ⑦ | Combine like terms: $$ \color{blue}{4x^2} + \color{red}{12x} + \color{green}{9} \color{blue}{-8x^2} \color{red}{-8x} + \color{green}{56} = \color{blue}{-4x^2} + \color{red}{4x} + \color{green}{65} $$ |
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