Răspuns:
1.
4x^2 + 4xy + y^2
9x^2 + 6xy + y^2
4x^2 + 12xy + 9y^2
9x^2 + 12xy + 4y^2
x^2 + 8xy + 16y^2
16x^2 + 24xy + 9y^2
2 + 2rad6 + 3 = 5 + 2rad6
9 + 12rad2 + 8 = 17 + 12rad2
3 + 8rad3 + 16 = 19 + 8rad3
8 + 20rad2 + 25 = 33 + 20rad2
12 + 12rad6 + 18 = 6(5 + 2rad6)
18 + 18rad6 + 27 = 9(5 + 2rad6)
2.
x^2 - 6xy + 9y^2
4x^2 - 8xy + 4y^2 = 4(x^2 - 2xy + y^2)
9x^2 - 12xy + 4y^2
16x^2 - 16xy + 4y^2
x^2 - 6xy + 9y^2
25x^2 - 30xy + 9y^2
1 - 2rad3 + 3 = 2(2 - rad3)
8 - 12rad2 + 9 = 17 - 12rad2
12 - 4rad6 + 2 = 2(7 - 2rad6)
9 - 6rad6 + 18 = 3(9 - 2rad6)
18 - 12rad6 + 12 = 6(5 - 2rad6)
3.
4x^2 - y^2
x^2 - 4y^2
9x^2 - 4y^2
4 - 3 = 1
7 - 4 = 3
20 - 18 = 2
4.
a)20 + 8rad5 + 4 + 5 - 8rad5 + 16 = 45
b)4x^2 + 4xy + y^2 + 9x^2 - 12xy - 4y^2 - 16x^2 - 8xy - y^2 =
-3x^2 - 16xy - 4y^2 = -(3x^2 + 16xy + 4y^2)
c)4x^2 - 12xy + 9y^2 - x^2 + 4y^2 + 9x^2 - 12xy + 4y^2 =
12x^2 - 24xy + 26y^2 =
2(6x^2 - 12xy + 13y^2)
d)4x^2 - y^2 + 4x^2 - 12xy + 9y^2 - x^2 + 4y^2 =
7x^2 - 12xy + 3y^2
e)5 - 2rad15 + 9 - 6 + 3 + 7 - 1 =
17 - 2rad15
