Question
Answer
$$((40-17x)x^2-3\cdot(3-x)(11x-6)^2)(-4x^2+19)-45x^3-200x\cdot(46-67x)=-1384x^5+5780x^4+1345x^3-12759x^2+15424x-6156$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}((40-17x)x^2-3\cdot(3-x)(11x-6)^2)(-4x^2+19)-45x^3-200x\cdot(46-67x)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}((40-17x)x^2-3\cdot(3-x)(121x^2-132x+36))(-4x^2+19)-45x^3-200x\cdot(46-67x) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(40x^2-17x^3-(9-3x)(121x^2-132x+36))(-4x^2+19)-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(40x^2-17x^3-(1089x^2-1188x+324-363x^3+396x^2-108x))(-4x^2+19)-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}(40x^2-17x^3-(-363x^3+1485x^2-1296x+324))(-4x^2+19)-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}(40x^2-17x^3+363x^3-1485x^2+1296x-324)(-4x^2+19)-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}(346x^3-1445x^2+1296x-324)(-4x^2+19)-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-1384x^5+5780x^4+1390x^3-26159x^2+24624x-6156-45x^3-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle9}{\textcircled {9}} } }}}-1384x^5+5780x^4+1345x^3-26159x^2+24624x-6156-(9200x-13400x^2) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle10}{\textcircled {10}} } }}}-1384x^5+5780x^4+1345x^3-26159x^2+24624x-6156-9200x+13400x^2 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle11}{\textcircled {11}} } }}}-1384x^5+5780x^4+1345x^3-12759x^2+15424x-6156\end{aligned} $$ | |
| ① | Find $ \left(11x-6\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ 11x } $ and $ B = \color{red}{ 6 }$. $$ \begin{aligned}\left(11x-6\right)^2 = \color{blue}{\left( 11x \right)^2} -2 \cdot 11x \cdot 6 + \color{red}{6^2} = 121x^2-132x+36\end{aligned} $$ |
| ② | $$ \left( \color{blue}{40-17x}\right) \cdot x^2 = 40x^2-17x^3 $$Multiply $ \color{blue}{3} $ by $ \left( 3-x\right) $ $$ \color{blue}{3} \cdot \left( 3-x\right) = 9-3x $$Multiply $ \color{blue}{200x} $ by $ \left( 46-67x\right) $ $$ \color{blue}{200x} \cdot \left( 46-67x\right) = 9200x-13400x^2 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{9-3x}\right) $ by each term in $ \left( 121x^2-132x+36\right) $. $$ \left( \color{blue}{9-3x}\right) \cdot \left( 121x^2-132x+36\right) = 1089x^2-1188x+324-363x^3+396x^2-108x $$ |
| ④ | Combine like terms: $$ \color{blue}{1089x^2} \color{red}{-1188x} +324-363x^3+ \color{blue}{396x^2} \color{red}{-108x} = -363x^3+ \color{blue}{1485x^2} \color{red}{-1296x} +324 $$ |
| ⑤ | Remove the parentheses by changing the sign of each term within them. $$ - \left( -363x^3+1485x^2-1296x+324 \right) = 363x^3-1485x^2+1296x-324 $$ |
| ⑥ | Combine like terms: $$ \color{blue}{40x^2} \color{red}{-17x^3} + \color{red}{363x^3} \color{blue}{-1485x^2} +1296x-324 = \color{red}{346x^3} \color{blue}{-1445x^2} +1296x-324 $$ |
| ⑦ | Multiply each term of $ \left( \color{blue}{346x^3-1445x^2+1296x-324}\right) $ by each term in $ \left( -4x^2+19\right) $. $$ \left( \color{blue}{346x^3-1445x^2+1296x-324}\right) \cdot \left( -4x^2+19\right) = \\ = -1384x^5+6574x^3+5780x^4-27455x^2-5184x^3+24624x+1296x^2-6156 $$ |
| ⑧ | Combine like terms: $$ -1384x^5+ \color{blue}{6574x^3} +5780x^4 \color{red}{-27455x^2} \color{blue}{-5184x^3} +24624x+ \color{red}{1296x^2} -6156 = \\ = -1384x^5+5780x^4+ \color{blue}{1390x^3} \color{red}{-26159x^2} +24624x-6156 $$ |
| ⑨ | Combine like terms: $$ -1384x^5+5780x^4+ \color{blue}{1390x^3} -26159x^2+24624x-6156 \color{blue}{-45x^3} = -1384x^5+5780x^4+ \color{blue}{1345x^3} -26159x^2+24624x-6156 $$ |
| ⑩ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 9200x-13400x^2 \right) = -9200x+13400x^2 $$ |
| ⑪ | Combine like terms: $$ -1384x^5+5780x^4+1345x^3 \color{blue}{-26159x^2} + \color{red}{24624x} -6156 \color{red}{-9200x} + \color{blue}{13400x^2} = \\ = -1384x^5+5780x^4+1345x^3 \color{blue}{-12759x^2} + \color{red}{15424x} -6156 $$ |
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