Question
Answer
$$8x-5\cdot(3+4x)+2x\cdot(6-x)+15=-2x^2$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}8x-5\cdot(3+4x)+2x\cdot(6-x)+15& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}8x-(15+20x)+12x-2x^2+15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}8x-15-20x+12x-2x^2+15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}-12x-15+12x-2x^2+15 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}-2x^2-15+15 \xlongequal{ } \\[1 em] & \xlongequal{ }-2x^2 -\cancel{15}+ \cancel{15} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-2x^2\end{aligned} $$ | |
| ① | Multiply $ \color{blue}{5} $ by $ \left( 3+4x\right) $ $$ \color{blue}{5} \cdot \left( 3+4x\right) = 15+20x $$Multiply $ \color{blue}{2x} $ by $ \left( 6-x\right) $ $$ \color{blue}{2x} \cdot \left( 6-x\right) = 12x-2x^2 $$ |
| ② | Remove the parentheses by changing the sign of each term within them. $$ - \left( 15+20x \right) = -15-20x $$ |
| ③ | Combine like terms: $$ \color{blue}{8x} -15 \color{blue}{-20x} = \color{blue}{-12x} -15 $$ |
| ④ | Combine like terms: $$ \, \color{blue}{ -\cancel{12x}} \,-15+ \, \color{blue}{ \cancel{12x}} \,-2x^2 = -2x^2-15 $$ |
| ⑤ | Combine like terms: $$ -2x^2 \, \color{blue}{ -\cancel{15}} \,+ \, \color{blue}{ \cancel{15}} \, = -2x^2 $$ |
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