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