You're studying factoring the difference of two squares

    A² - B² = (A - B)(A + B)

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1.    3x² - 3(x+2)²

First take out the common factor 3, using []'s

  3[x² - (x+2)²]   

Now factor the expression in the []'s as the difference 
of two squares:

 3[x - (x+2)][x + (x+2)]

Simplify:

 3[x - x - 2][x + x + 2]

 3[-2][2x+2]

Multiply the 3 by the -2 and also take out common
factor 2

   -6[2(x+1)] 

    -12(x+1)

That's it.

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2.    12x²-27(3+x)²


   First take out the common factor 3, using []'s

  3[4x² - 9(3+x)²]   

Now factor the expression in the []'s as the difference 
of two squares:

 3[2x - 3(3+x)][2x + 3(3+x)]

Simplify:

 3[2x - 9 - 3x][2x + 9 + 3x]

 3[-x - 9][5x + 9]

Take out common factor -1 in [-x - 9]

 3(-1)[x + 9][5x + 9]
 
   -3(x + 9)(5x + 9)

That's it.

Edwin