(1)ab(x+y)(x-y)-xy(a+b)(a-b) (2)x^4+x^2-2ax+1-a^2 (3)a^4-a^2+4a-4
问题描述：
(1)ab(x+y)(x-y)-xy(a+b)(a-b) (2)x^4+x^2-2ax+1-a^2 (3)a^4-a^2+4a-4
答
(3)a^4-a^2+4a-4
=a^4-(a^2-4a+4)
=(a^2)^2-(a-2)^2
=(a^2+a-2)(a^2-a+2)
答
(1)ab(x+y)(x-y)-xy(a+b)(a-b) =abxx-abyy-xyaa+xybb=ax（bx-ay）+by（bx-ay）
=(bx-ay)(ax+by)
(2)x^4+x^2-2ax+1-a^2 = =-(a^2+2aX+X^2) + 1+X^4+2X^2-2X^2
=-(a+X)^2+2X^2 + (1+X^2)^2-2X^2 =(x^2-x+1-a)(x^2+x+1+a)
(3)a^4-a^2+4a-4=(a^4-a^2)+(4a-4)=a^2(aa-1)+4(a-1)=(a-1)(a^3+a^2+4)=(a-1)(a+2)(a^2-a+2)
答
ab(x+y)(x-y)-xy(a+b)(a-b)=ab(x^2-y^2)-xy(a^2-b^2)=abx^2-aby^2-xya^2+xyb^2=ax(bx-ay)-by(ay-bx)=ax(bx-ay)+by(bx-ay)=(ax+by)(bx-ay)x^4+x^2-2ax+1-a^2=x^4+2x^2+1-(x^2-2ax+a^2)=(x^2+1)^2-(x-a)^2=(x^2+1+x-a)...