Simplify $(x^2-2x-x+2)(x-3)$ [closed]

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Simplify $(x^2-2x-x+2)(x-3)$.

So here is my take on it (might me wrong correct me if I am wrong)

$$x^3-3x^2-2x^2+6x-x^2+3x+2x-6.$$

Now, what should I do?

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2 Answers

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Probably, the idea is to use the fact that\begin{align}x^2-2x-x+2&=x(x-2)-(x-2)\\&=(x-1)(x-2).\end{align}And therefore your whole expression is equal to $(x-1)(x-2)(x-3)$.

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$$ (x-3)(x^{2} - 2x - x + 2) = (x-3)(x(x-2) - (x-2)) = (x-3)((x-2)(x-1)) = (x-3)(x-2)(x-1). $$Notice that $-2x - x = -3x,$ yet it was not written as $-3x$ which should have sparked suspicion.

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