Question
Answer
$$(x-2)(x-2)(x-1)=x^3-5x^2+8x-4$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)(x-2)(x-1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}(x^2-2x-2x+4)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}(x^2-4x+4)(x-1) \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}x^3-x^2-4x^2+4x+4x-4 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle4}{\textcircled {4}} } }}}x^3-5x^2+8x-4\end{aligned} $$ | |
| ① | Multiply each term of $ \left( \color{blue}{x-2}\right) $ by each term in $ \left( x-2\right) $. $$ \left( \color{blue}{x-2}\right) \cdot \left( x-2\right) = x^2-2x-2x+4 $$ |
| ② | Combine like terms: $$ x^2 \color{blue}{-2x} \color{blue}{-2x} +4 = x^2 \color{blue}{-4x} +4 $$ |
| ③ | Multiply each term of $ \left( \color{blue}{x^2-4x+4}\right) $ by each term in $ \left( x-1\right) $. $$ \left( \color{blue}{x^2-4x+4}\right) \cdot \left( x-1\right) = x^3-x^2-4x^2+4x+4x-4 $$ |
| ④ | Combine like terms: $$ x^3 \color{blue}{-x^2} \color{blue}{-4x^2} + \color{red}{4x} + \color{red}{4x} -4 = x^3 \color{blue}{-5x^2} + \color{red}{8x} -4 $$ |
This page was created using
Simplify polynomials calculator