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(x^2-b^2+y^2-a^2)^2-4(ab-xy)^2因式分解

题目详情
(x^2-b^2+y^2-a^2)^2-4(ab-xy)^2因式分解
▼优质解答
答案和解析
(x^2-b^2+y^2-a^2)^2-4(ab-xy)^2
=[(x²-b²+y²-a²)+2(ab-xy)][(x²-b²+y²-a²)-2(ab-xy)]
=[(x²-2xy+y²)-(a²-2ab+b²)][(x²+2xy+y²)-(a²+2ab+b²)]
=[(x-y)²-(a-b)²][(x+y)²-(a+b)²]
=(x-y+a-b)(x-y-a+b)(x+y+a+b)(x+y-a-b)