Question
Answer
$$7(x-3)-1-7x(x-3)-2=-7x^2+28x-24$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}7(x-3)-1-7x(x-3)-2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}7x-21-1-(7x^2-21x)-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}7x-22-(7x^2-21x)-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}7x-22-7x^2+21x-2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-7x^2+28x-24\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{7} $ by $ \left( x-3\right) $ $$ \color{blue}{7} \cdot \left( x-3\right) = 7x-21 $$Multiply $ \color{blue}{7x} $ by $ \left( x-3\right) $ $$ \color{blue}{7x} \cdot \left( x-3\right) = 7x^2-21x $$ |
| ② | Combine like terms: $$ 7x \color{blue}{-21} \color{blue}{-1} = 7x \color{blue}{-22} $$ |
| ③ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 7x^2-21x \right) = -7x^2+21x $$ |
| ④ | Combine like terms: $$ \color{blue}{7x} \color{red}{-22} -7x^2+ \color{blue}{21x} \color{red}{-2} = -7x^2+ \color{blue}{28x} \color{red}{-24} $$ |
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