Question 221507
I have to factor each trinomial


{{{3x^3y^2-3x^2y^2+3xy^2}}}


Can someone please help me understand this equation.

Thanks


Step 1.  Find a factor common to all three terms.  Start with a number 3 since it's common to all three terms and we factor 3 out.


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

Step 2.  Now look at the x-terms with the highest exponent in x that is common to all three terms.  In this case, it's simply x and we factor x out.


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


Step 3.  Now look at the y-terms and we observe that {{{y^2}}} is common to all three terms and we factor {{{y^2}}} out.


{{{3x(x^2y^2-3xy^2+y^2)=3xy^2(x^2-3x+1)}}}


Step 4.  ANSWER:  {{{3x^3y^2-3x^2y^2+3xy^2=3xy^2(x^2-3x+1)}}}


I hope the above steps were helpful.


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Good luck in your studies!


Respectfully,
Dr J