Question
Answer
$$(40-x)((28-x)\cdot(14-x)-144)-20(20-14x)\cdot30-18\cdot(240+18\cdot(28-x))=-x^3+82x^2+6796x-15472$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(40-x)((28-x)\cdot(14-x)-144)-20(20-14x)\cdot30-18\cdot(240+18\cdot(28-x))& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(40-x)(392-28x-14x+x^2-144)-20\cdot(600-420x)-18\cdot(240+504-18x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(40-x)(x^2-42x+248)-20\cdot(600-420x)-18\cdot(240+504-18x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(40-x)(x^2-42x+248)-20\cdot(600-420x)-18(-18x+744) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}40x^2-1680x+9920-x^3+42x^2-248x-(12000-8400x)-(-324x+13392) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-x^3+82x^2-1928x+9920-(12000-8400x)-(-324x+13392) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-x^3+82x^2-1928x+9920-12000+8400x-(-324x+13392) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-x^3+82x^2+6472x-2080-(-324x+13392) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-x^3+82x^2+6472x-2080+324x-13392 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}-x^3+82x^2+6796x-15472\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{28-x}\right) $ by each term in $ \left( 14-x\right) $. $$ \left( \color{blue}{28-x}\right) \cdot \left( 14-x\right) = 392-28x-14x+x^2 $$$$ \left( \color{blue}{20-14x}\right) \cdot 30 = 600-420x $$Multiply $ \color{blue}{18} $ by $ \left( 28-x\right) $ $$ \color{blue}{18} \cdot \left( 28-x\right) = 504-18x $$ |
| ② | Combine like terms: $$ \color{blue}{392} \color{red}{-28x} \color{red}{-14x} +x^2 \color{blue}{-144} = x^2 \color{red}{-42x} + \color{blue}{248} $$ |
| ③ | Combine like terms: $$ \color{blue}{240} + \color{blue}{504} -18x = -18x+ \color{blue}{744} $$ |
| ④ | Multiply each term of $ \left( \color{blue}{40-x}\right) $ by each term in $ \left( x^2-42x+248\right) $. $$ \left( \color{blue}{40-x}\right) \cdot \left( x^2-42x+248\right) = 40x^2-1680x+9920-x^3+42x^2-248x $$Multiply $ \color{blue}{20} $ by $ \left( 600-420x\right) $ $$ \color{blue}{20} \cdot \left( 600-420x\right) = 12000-8400x $$Multiply $ \color{blue}{18} $ by $ \left( -18x+744\right) $ $$ \color{blue}{18} \cdot \left( -18x+744\right) = -324x+13392 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{40x^2} \color{red}{-1680x} +9920-x^3+ \color{blue}{42x^2} \color{red}{-248x} = -x^3+ \color{blue}{82x^2} \color{red}{-1928x} +9920 $$ |
| ⑥ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 12000-8400x \right) = -12000+8400x $$ |
| ⑦ | Combine like terms: $$ -x^3+82x^2 \color{blue}{-1928x} + \color{red}{9920} \color{red}{-12000} + \color{blue}{8400x} = -x^3+82x^2+ \color{blue}{6472x} \color{red}{-2080} $$ |
| ⑧ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -324x+13392 \right) = 324x-13392 $$ |
| ⑨ | Combine like terms: $$ -x^3+82x^2+ \color{blue}{6472x} \color{red}{-2080} + \color{blue}{324x} \color{red}{-13392} = -x^3+82x^2+ \color{blue}{6796x} \color{red}{-15472} $$ |
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