1.
(2x^2-3x-1)^2-22x^2+33x+11-12
=(2x^2-3x-1)^2-11(2x^2-3x-1)-12
=(2x^2-3x-1+1)(2x^2-3x-1-12)
=(2x^2-3x)(2x^2-3x-13)
=x(2x-3)(2x^2-3x-13)
2.
(6x+7)^2(3x+4)(x+1)-6
=(36x^2+84x+49)(3x^2+7x+4)-6
=108x^4+252x^3+144x^2+252x^3+588x^2+336x+147x^2+343x+196-6
=108x^4+504x^3+291x^2+679x+190
=
3.
(a+b-2ab)(a+b-2)+(1-ab)^2
=(a+b)^2-2(a+b)-2ab(a+b)+4ab+(1-ab)^2
=(a+b)^2-2(a+b)(1+2ab)+(1+ab)^2
=(a+b-1-ab)^2
=(a-1)^2(b-1)^2
(x+1)(x+6)(x+2)(x+3)+x^2
=(x^2+7x+6)(x^2+5x+6)+x^2
=(x^2+6)^2+12x(x^2+6)+35x^2+x^2
=(x^2+6)^2+12x(x^2+6)+36x^2
=(x^2+6+6x)^2
(a-b)(x-y)(x+y)-(x-y)(a-b)(a+b)
=(a-b)(x-y)(x+y-a-b)