Question
Answer
$$5x^3+4x^2+6x-3-2x^3+3x^2-7x+9-(5x+3)(4x^2+x-1)=-17x^3-10x^2+x+9$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}5x^3+4x^2+6x-3-2x^3+3x^2-7x+9-(5x+3)(4x^2+x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}3x^3+7x^2-x+6-(5x+3)(4x^2+x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}3x^3+7x^2-x+6-(20x^3+5x^2-5x+12x^2+3x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}3x^3+7x^2-x+6-(20x^3+17x^2-2x-3) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}3x^3+7x^2-x+6-20x^3-17x^2+2x+3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}-17x^3-10x^2+x+9\end{aligned} $$ | |
| ① | Combine like terms: $$ \color{blue}{5x^3} + \color{red}{4x^2} + \color{green}{6x} \color{orange}{-3} \color{blue}{-2x^3} + \color{red}{3x^2} \color{green}{-7x} + \color{orange}{9} = \\ = \color{blue}{3x^3} + \color{red}{7x^2} \color{green}{-x} + \color{orange}{6} $$ |
| ② | Multiply each term of $ \left( \color{blue}{5x+3}\right) $ by each term in $ \left( 4x^2+x-1\right) $. $$ \left( \color{blue}{5x+3}\right) \cdot \left( 4x^2+x-1\right) = 20x^3+5x^2-5x+12x^2+3x-3 $$ |
| ③ | Combine like terms: $$ 20x^3+ \color{blue}{5x^2} \color{red}{-5x} + \color{blue}{12x^2} + \color{red}{3x} -3 = 20x^3+ \color{blue}{17x^2} \color{red}{-2x} -3 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( 20x^3+17x^2-2x-3 \right) = -20x^3-17x^2+2x+3 $$ |
| ⑤ | Combine like terms: $$ \color{blue}{3x^3} + \color{red}{7x^2} \color{green}{-x} + \color{orange}{6} \color{blue}{-20x^3} \color{red}{-17x^2} + \color{green}{2x} + \color{orange}{3} = \\ = \color{blue}{-17x^3} \color{red}{-10x^2} + \color{green}{x} + \color{orange}{9} $$ |
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