Question
Answer
$$(65-x)(5x^2-34x+2)^2-283(x-1)(xxx+3)=-25x^5+1682x^4-22993x^3+76576x^2-9693x+1109$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(65-x)(5x^2-34x+2)^2-283(x-1)(xxx+3)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(65-x)(5x^2-34x+2)^2-283(x-1)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}(65-x)(25x^4-340x^3+1176x^2-136x+4)-283(x-1)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-25x^5+1965x^4-23276x^3+76576x^2-8844x+260-(283x-283)(x^3+3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}-25x^5+1965x^4-23276x^3+76576x^2-8844x+260-(283x^4+849x-283x^3-849) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}-25x^5+1965x^4-23276x^3+76576x^2-8844x+260-283x^4-849x+283x^3+849 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle8}{\textcircled {8}} } }}}-25x^5+1682x^4-22993x^3+76576x^2-9693x+1109\end{aligned} $$ | |
| ① | $$ x x x = x^{1 + 1 + 1} = x^3 $$ |
| ② | Multiply each term of $ \left( \color{blue}{5x^2-34x+2}\right) $ by each term in $ \left( 5x^2-34x+2\right) $. $$ \left( \color{blue}{5x^2-34x+2}\right) \cdot \left( 5x^2-34x+2\right) = 25x^4-170x^3+10x^2-170x^3+1156x^2-68x+10x^2-68x+4 $$ |
| ③ | Combine like terms: $$ 25x^4 \color{blue}{-170x^3} + \color{red}{10x^2} \color{blue}{-170x^3} + \color{green}{1156x^2} \color{orange}{-68x} + \color{green}{10x^2} \color{orange}{-68x} +4 = \\ = 25x^4 \color{blue}{-340x^3} + \color{green}{1176x^2} \color{orange}{-136x} +4 $$ |
| ④ | Multiply each term of $ \left( \color{blue}{65-x}\right) $ by each term in $ \left( 25x^4-340x^3+1176x^2-136x+4\right) $. $$ \left( \color{blue}{65-x}\right) \cdot \left( 25x^4-340x^3+1176x^2-136x+4\right) = \\ = 1625x^4-22100x^3+76440x^2-8840x+260-25x^5+340x^4-1176x^3+136x^2-4x $$ |
| ⑤ | Combine like terms: $$ \color{blue}{1625x^4} \color{red}{-22100x^3} + \color{green}{76440x^2} \color{orange}{-8840x} +260-25x^5+ \color{blue}{340x^4} \color{red}{-1176x^3} + \color{green}{136x^2} \color{orange}{-4x} = \\ = -25x^5+ \color{blue}{1965x^4} \color{red}{-23276x^3} + \color{green}{76576x^2} \color{orange}{-8844x} +260 $$Multiply $ \color{blue}{283} $ by $ \left( x-1\right) $ $$ \color{blue}{283} \cdot \left( x-1\right) = 283x-283 $$ |
| ⑥ | Multiply each term of $ \left( \color{blue}{283x-283}\right) $ by each term in $ \left( x^3+3\right) $. $$ \left( \color{blue}{283x-283}\right) \cdot \left( x^3+3\right) = 283x^4+849x-283x^3-849 $$ |
| ⑦ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 283x^4+849x-283x^3-849 \right) = -283x^4-849x+283x^3+849 $$ |
| ⑧ | Combine like terms: $$ -25x^5+ \color{blue}{1965x^4} \color{red}{-23276x^3} +76576x^2 \color{green}{-8844x} + \color{orange}{260} \color{blue}{-283x^4} \color{green}{-849x} + \color{red}{283x^3} + \color{orange}{849} = \\ = -25x^5+ \color{blue}{1682x^4} \color{red}{-22993x^3} +76576x^2 \color{green}{-9693x} + \color{orange}{1109} $$ |
This page was created using
Simplify polynomials calculator