问题标题：
因式分解：(a+b)^3-(a+b)a^2(x-y)^2-b^2(y-x)^2(5a^2-2b^2)^2-(2a^2-5b^2)^2用简便方法计算：57^2×0.01-43^2×0.01
问题描述：
因式分解：(a+b)^3-(a+b)
a^2(x-y)^2-b^2(y-x)^2
(5a^2-2b^2)^2-(2a^2-5b^2)^2
用简便方法计算：
57^2×0.01-43^2×0.01
史海峰回答：
(a+b)"'-(a+b)
=(a+b)[(a+b)"-1]
=(a+b)[(a+b)"-1"]
=(a+b)(a+b+1)(a+b-1)
a"(x-y)"-b"(y-x)"
=[a(x-y)]"-[b(x-y)]"
=[(ax-ay)+(bx-by)][(ax-ay)-(bx-by)]
=(ax-ay+bx-by)(ax-ay-bx+by)
(5a"-2b")"-(2a"-5b")"
=[(5a"-2b")+(2a"-5b")][(5a"-2b")-(2a"-5b")]
=(5a"-2b"+2a"-5b")(5a"-2b"-2a"+5b")
=(7a"-7b")(3a"+3b")
=21(a"+b")(a+b)(a-b)
57"X0.01-43"X0.01
=5.7"-4.3"
=(5.7-4.3)(5.7+4.3)
=1.4X10
=14
或者
=0.01X(57"-43")
=0.01X(57+43)(57-43)
=0.01X100X14
=14
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