How to factor the trinomial : $ xy-x+y-1$ ? The factorization is $(x+1)(y-1) $ but I don't where it comes from.
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1About factoring such kind of expressions: http://math.stackexchange.com/a/544042/11206 – miracle173 Jun 04 '16 at 09:04
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You can search for "Simon's favourite factoring trick" for the "general" case. – MonadBoy Jun 04 '16 at 09:09
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It is not easy in general to factor multivariate polynomials because they are in general not uniquely factor-able. – mathreadler Jun 04 '16 at 10:07
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$$xy-x+y-1=\color{green}{x}\cdot\color{red}{(y-1)}\color{green}{+1}\cdot\color{red}{(y-1)}=\color{green}{(x+1)}\color{red}{(y-1)}$$ Or $$xy-x+y-1=xy+y-x-1=\color{red}{(x+1)}\cdot \color{green}{y}+\color{red}{(x+1)}\cdot\color{green}{-1}=\color{red}{(x+1)}\color{green}{(y-1)}$$
b00n heT
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Basically you are to look for 2 terms such that when you take common from them and common from other two terms you get same expression in bracket
Gathdi
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Remember always one thing that such trinomial always give something like $(x ? 1)(y ? 1)$ where "?" refer to the suitable sign ($+ or -$). Whenever you stuck in solving/factoring such trinomial, just do the following:
$xy-x+y-1=(x ? 1)(y ? 1)$ (As I said above).
Now notice that $x$ has got negative sign and $y$ has gt positive sign, so $1$ with which y is multiplied is positive and other one is negative. Just replace the $?$ now and you get, $xy-x+y-1=(x + 1)(y - 1)$.
Consider an other example: If you are asked to factorise $xy-x-y+1$ then as stated, write it as $(x?1)(y?1)$. Now notice that both $x$ and $y$ has got negative sign so both $1's$ are negative and hence $xy-x-y+1=(x-1)(y-1)$
Vidyanshu Mishra
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