Question
Answer
$$(x-2)^2+(x-1)^3=x^3-2x^2-x+3$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(x-2)^2+(x-1)^3& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}x^2-4x+4+x^3-3x^2+3x-1 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}x^3-2x^2-x+3\end{aligned} $$ | |
| ① | Find $ \left(x-2\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}{ 2 }$. $$ \begin{aligned}\left(x-2\right)^2 = \color{blue}{x^2} -2 \cdot x \cdot 2 + \color{red}{2^2} = x^2-4x+4\end{aligned} $$Find $ \left(x-1\right)^3 $ using formula $$ (A - B) = A^3 - 3A^2B + 3AB^2 - B^3 $$where $ A = x $ and $ B = 1 $. $$ \left(x-1\right)^3 = x^3-3 \cdot x^2 \cdot 1 + 3 \cdot x \cdot 1^2-1^3 = x^3-3x^2+3x-1 $$ |
| ② | Combine like terms: $$ \color{blue}{x^2} \color{red}{-4x} + \color{green}{4} +x^3 \color{blue}{-3x^2} + \color{red}{3x} \color{green}{-1} = x^3 \color{blue}{-2x^2} \color{red}{-x} + \color{green}{3} $$ |
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