Question
Answer
$$(x-2)(x^2-3x+3)-(x-1)^2+3(x-1)-3=x^3-6x^2+14x-13$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x^2-3x+3)-(x-1)^2+3(x-1)-3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x-2)(x^2-3x+3)-(x^2-2x+1)+3(x-1)-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-3x^2+3x-2x^2+6x-6-(x^2-2x+1)+3x-3-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-5x^2+9x-6-(x^2-2x+1)+3x-3-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-5x^2+9x-6-x^2+2x-1+3x-3-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle5}{\textcircled {5}} } }}}x^3-6x^2+11x-7+3x-3-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle6}{\textcircled {6}} } }}}x^3-6x^2+14x-10-3 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle7}{\textcircled {7}} } }}}x^3-6x^2+14x-13\end{aligned} $$ | |
| ① | Find $ \left(x-1\right)^2 $ using formula. $$ (A - B)^2 = \color{blue}{A^2} - 2 \cdot A \cdot B + \color{red}{B^2} $$where $ A = \color{blue}{ x } $ and $ B = \color{red}{ 1 }$. $$ \begin{aligned}\left(x-1\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 1 + \color{red}{1^2} = x^2-2x+1\end{aligned} $$ |
| ② | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x^2-3x+3\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x^2-3x+3\right) = x^3-3x^2+3x-2x^2+6x-6 $$Multiply $ \color{blue}{3} $ by $ \left( x-1\right) $ $$ \color{blue}{3} \cdot \left( x-1\right) = 3x-3 $$ |
| ③ | Combine like terms: $$ x^3 \color{blue}{-3x^2} + \color{red}{3x} \color{blue}{-2x^2} + \color{red}{6x} -6 = x^3 \color{blue}{-5x^2} + \color{red}{9x} -6 $$ |
| ④ | Remove the parentheses by changing the sign of each term within them. $$ - \left( x^2-2x+1 \right) = -x^2+2x-1 $$ |
| ⑤ | Combine like terms: $$ x^3 \color{blue}{-5x^2} + \color{red}{9x} \color{green}{-6} \color{blue}{-x^2} + \color{red}{2x} \color{green}{-1} = x^3 \color{blue}{-6x^2} + \color{red}{11x} \color{green}{-7} $$ |
| ⑥ | Combine like terms: $$ x^3-6x^2+ \color{blue}{11x} \color{red}{-7} + \color{blue}{3x} \color{red}{-3} = x^3-6x^2+ \color{blue}{14x} \color{red}{-10} $$ |
| ⑦ | Combine like terms: $$ x^3-6x^2+14x \color{blue}{-10} \color{blue}{-3} = x^3-6x^2+14x \color{blue}{-13} $$ |
This page was created using
Simplify polynomials calculator