=x^3-x^2+x- 1

=(x- 1)^3+2x^2-2x

=(x- 1)^3+2x(x- 1)

=(x- 1)[(x- 1)^2+2x]

=(x- 1)(x^2+ 1)

(2) the square of x+4 (xy-1)+the square of 4 y.

=x^2+4(xy- 1)+4y^2

=(x+2y)^2-4

=(x+2y+2)(x+2y-2)

(3)x cube y squared cube (x-y)-x cube y squared cube (y -x)

=x^3y^2(x-y)^3-x^2y^3(y-x)^3

=(xy)^2[x(x-Y)^3+y(x-y)^3]

=(xy)^2(x-y)^3(x+y)

(4)A-2a cube B cube +b6 cube to the 6th power

=a^6-2a^3b^3+b^6

=(a^3-b^3)^2

=[(a-b)(a^2+ab+b^2]^2

(5)a cube X cube +x cube -a cube Y cube -y cube

=a^3x^3+x^3-a^3y^3-y^3

=a^3(x^3-y^3)+(x^3-y^3)

=(x^3-y^3)(a^3+ 1)

=(x-y)(x^2+xy+y^2)(a+ 1)(a^2-a+ 1)

(6) Square of A- square of B-AC+BC

=a^2-b^2-ac+bc

=(a+b)(a-b)-c(a-b)

=(a-b)(a+b-c)

The square of (8) (x square +6x+6) +x square +6x+4

=(x^2+6x+6)^2+(x^2+6x+6)-2

=(x^2+6x+8)(x^2+6x+5)

=(x+4)(x+2)(x+ 1)(x+5)。