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hi, please help me to answer this question.

Show that Det M = (a-b) (b-c) ( c-a), when the equation is like this [ bc² - cb² - ac² + a²c + ab² - ba²]
Reply 1
If you half expand the first expression
(ab - ac -b^2 + bc) (c - a)
then you should be able to see how to factorize the 2nd expression to end up with the right result? Two terms cancel when you fully expand this expression.
Original post by Frhh
Show that Det M = (a-b) (b-c) ( c-a), when the equation is like this [ bc² - cb² - ac² + a²c + ab² - ba²]


As mqb said above, it's probably easier to expand the factorised form and show that it's equal to the expression you have.
Reply 3
Show that Det M = (a-b) (b-c) ( c-a), when the equation is like this [ bc² - cb² - ac² a²c ab² - ba²]
Reply 4
Original post by mqb2766
If you half expand the first expression
(ab - ac -b^2 + bc) (c - a)
then you should be able to see how to factorize the 2nd expression to end up with the right result? Two terms cancel when you fully expand this expression.




Can you give me another method? Cause I'm not pretty sure either we can use the method that you give
Reply 5
Original post by Frhh
Can you give me another method? Cause I'm not pretty sure either we can use the method that you give


If you've just got to show that the two expressions are the same, then either
* expand the factorized expression
* factorize the expanded expression
I was simply saying if you're finding the 2nd way difficult, use the first method to see how terms are grouped etc and reverse engineer the steps.

For instance, a simple observation is that the factorized expression has 8 terms when expanded, but the expanded expression has only 6. So you must have to introduce two extra terms (one positive and one negative, so they sum to zero). Once you introduce those two extra terms, you should be able to pull the factors
(a-b)
(b-c)
out in order?

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