Question
Answer
$$(4x-7)(x+3)-(x-1)(x+8)=3x^2-2x-13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4x-7)(x+3)-(x-1)(x+8)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4x^2+12x-7x-21-(x^2+8x-x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}4x^2+5x-21-(x^2+7x-8) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}4x^2+5x-21-x^2-7x+8 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^2-2x-13\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{4x-7}\right) $ by each term in $ \left( x+3\right) $. $$ \left( \color{blue}{4x-7}\right) \cdot \left( x+3\right) = 4x^2+12x-7x-21 $$Multiply each term of $ \left( \color{blue}{x-1}\right) $ by each term in $ \left( x+8\right) $. $$ \left( \color{blue}{x-1}\right) \cdot \left( x+8\right) = x^2+8x-x-8 $$ |
| ② | Combine like terms: $$ 4x^2+ \color{blue}{12x} \color{blue}{-7x} -21 = 4x^2+ \color{blue}{5x} -21 $$Combine like terms: $$ x^2+ \color{blue}{8x} \color{blue}{-x} -8 = x^2+ \color{blue}{7x} -8 $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2+7x-8 \right) = -x^2-7x+8 $$ |
| ④ | Combine like terms: $$ \color{blue}{4x^2} + \color{red}{5x} \color{green}{-21} \color{blue}{-x^2} \color{red}{-7x} + \color{green}{8} = \color{blue}{3x^2} \color{red}{-2x} \color{green}{-13} $$ |
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