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