作业帮(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
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(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
(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
(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
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)(x^2+1-x+a)
a^4-a^2+4a-4
=a^4-(a^2-4a+4)
=a^4-(a-2)^2
=(a^2+a-2)(a^2-a+2)
=(a+2)(a-1)(a^2-a+2)
(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)
(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)