a: =4(x-2)(x+1)+4(x-2)^2+(x+1)^2
=(2x-4)^2+2*(2x-4)(x+1)+(x+1)^2
=(2x-4+x+1)^2=(3x-3)^2=9(x-1)^2
b: =x^7(x^2-1)-x^5(x+1)+x^3(x+1)+(x^2-1)
=(x+1)[x^7(x-1)-x^5+x^3+x-1]
=(x+1)[x^7(x-1)-x^3(x-1)(x+1)+(x-1)]
=(x+1)(x-1)(x^7-x^4-x^3+1)
=(x+1)(x-1)(x^3-1)(x^4-1)
=(x+1)(x-1)^2*(x^2+x+1)(x^2+1)(x-1)(x+1)
=(x+1)^2*(x-1)^3*(x^2+1)(x^2+x+1)