Question 103829
{{{12x^2y^2 + 10xy^2}}} - {{{42y^2) }}}  

{{{2y^2}}} is a common factor of all three terms, so pull it out

{{{2y^2(6x^2 + 5x - 21) }}}

now we can factor {{{6x^2 + 5x - 21 }}}

replace {{{5x}}}with {{{-9x + 14x}}}

now we have {{{6x^2 - 9x + 14x - 21 }}} group the first two terms together and the last  two terms 

now we have {{{(6x^2 - 9x) + (14x - 21) }}} 

  {{{3x}}} is a common factor of both terms in the first group, and {{{7}}} is a common factor in the second group; so,  pull it out and you will have

{{{3x(2x - 3) + 7(2x - 3) }}} 

{{{2x - 3}}} is a common factor of both terms; so, factor it out and you will have

{{{(2x - 3)(3x + 7)}}}


now go back to {{{2y^2(6x^2 + 5x - 21) }}} and substitute {{{6x^2 + 5x - 21 }}}
 with {{{(2x - 3)(3x + 7)}}}
 
and you will have:
{{{2y^2(2x - 3)(3x + 7)}}}