x^3-4xy^2-2x^2y+8y^3
=x^2(x-2y)-4y^2(x-2y)
=(x-2y)(x^2-4y^2)
=(x-2y)^2(x+2y)
（x^2+x）^2-8(x^2+x)+12
=（x^2+x-6)(x^2+x-2)
=(x+3)(x-2)(x+2)(x-1)
12x^2-5x-2
=12x^2+3x-8x-2
=3x(4x+1)-2(4x+1)
=(3x-2)(4x+1)
5x^2+6xy－8y^2
=(x+2y)(5x－4y).
x^4+64
=x^4+16x^2+64-16x^2
=(x^2+8)^2-16x^2
=(x^2+4x+8)(x^2-4x+8)
x³-11x²+31x-21
=(x³-x²)-(10x²-10x)+(21x-21)
=x²(x-1)-10x(x-1)+21(x-1)
=(x²-10x+21)(x-1)
=(x-3)(x-7)(x-1)
=(x-1)(x-3)(x-7)
3a3b-81b4
=3b(a^3-27b^3)
=3b(a-3b)(a^2+3ab+9b^2)
a7-ab6
=a(a^6-b^6)
=a(a^3+b^3)(a^3-b^3)
=a(a-b)(a^2+ab+b^2)(a+b)(a^2-ab+b^2)
ab(c^2-d^2)+cd(a^2-b^2)
=abc^2-abd^2+a^2cd-cb^2d
=abc^2+a^2cd-cb^2d-abd^2
=ac(bc+ad)-bd(cb+ad)
=(bc+ad)(ac-bd)
4x^4-13x^2+9
=（4x^2-9）(x^2-1)
=(2x+3)(2x-3)(x+1)(x-1)
(x^2-2x)^2-7(x2-2x)+12
=(x^2-2x-4)(x^2-2x-3)
=(x^2-2x-4)(x-3)(x+1)
x^2+x-(a^2-a)
=x^2-a^2+x-a
=(x-a)(x+a)+x-a
=(x-a)(x+a+1)
