Question
Answer
$$4(x-3)^2-(3x+2)^2=-5x^2-36x+32$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}4(x-3)^2-(3x+2)^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4(x^2-6x+9)-(9x^2+12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2-24x+36-(9x^2+12x+4) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2-24x+36-9x^2-12x-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-5x^2-36x+32\end{aligned} $$ | |
| ① | Find $ \left(x-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}{ x } $ and $ B = \color{red}{ 3 }$. $$ \begin{aligned}\left(x-3\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 3 + \color{red}{3^2} = x^2-6x+9\end{aligned} $$Find $ \left(3x+2\right)^2 $ using formula. $$ (A + B)^2 = \color{blue}{A^2} + 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 3x } $ and $ B = \color{red}{ 2 }$. $$ \begin{aligned}\left(3x+2\right)^2 = \color{blue}{\left( 3x \right)^2} +2 \cdot 3x \cdot 2 + \color{red}{2^2} = 9x^2+12x+4\end{aligned} $$ |
| ② | Multiply $ \color{blue}{4} $ by $ \left( x^2-6x+9\right) $ $$ \color{blue}{4} \cdot \left( x^2-6x+9\right) = 4x^2-24x+36 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9x^2+12x+4 \right) = -9x^2-12x-4 $$ |
| ④ | Combine like terms: $$ \color{blue}{4x^2} \color{red}{-24x} + \color{green}{36} \color{blue}{-9x^2} \color{red}{-12x} \color{green}{-4} = \color{blue}{-5x^2} \color{red}{-36x} + \color{green}{32} $$ |
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