Question 217339
{{{3x^2-29xy+18y^2}}}


I assume this problem is a factoring problem


Step 1.  Need to find two integers m and n such that their sum m+n=-29 and their product is m*n=3*18=54.


Step 2.  After a couple tries, the integers are -2 and -27.


Step 3.  We can now factor the equation using grouping and noting that {{{-29xy=-2xy-27xy}}}.


{{{3x^2-29xy+18y^2=(3x^2-2xy)+1*(-27xy+18y^2)}}}


Factor x in the first group and -9y in the second group


{{{3x^2-29xy+18y^2=x(3x-2y)-9y(3x-2y)}}}


Now factor 3x-2y since it is common to both groups


{{{3x^2-29xy+18y^2=(3x-2y)(x-9y)}}}



Step 4.  ANSWER:  {{{3x^2-29xy+18y^2=(3x-2y)(x-9y)}}}


I hope the above steps and explanation were helpful. 


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Also, good luck in your studies and contact me at john@e-liteworks.com for your future math needs.


Respectfully, 
Dr J