Expand (x+y-z)²
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( x + y - z)²
Using the identity :
( a + b + c)² = a² + b² + c² + 2ab + 2bc + 2ca
( x + y - z)² can also be written in the form :
- [x + y + (- z)]²
= x² + y² + (-z)² + 2 xy + 2 y (-z) + 2 (-z) x
= x² + y² + z² + 2xy - 2yz - 2zx
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From the above result , we could conclude that we can identify the term which is negetive by seeing the common term .
For example :
In above result , 2yz and 2zx are in negetive having the common variable z .
Hence the variable with negetive value is z .
In this way , we can even factorise the given answer .
For example :
If the question is factorise a² + b² + c² - 2ab - 2bc + 2ac , our answer would be : ( a - b + c)² because in this , the terms 2ab and 2 bc are negetive having common b . Hence b is a negetive variable .
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