因式分解,求解(第六题)
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(6),(c²-b²+d²-a²)²-4(ab-cd)²
=(c²-b²+d²-a²+2(ab-cd))(c²-b²+d²-a²-2(ab-cd))
=((c-d)²-(a-b)²)((c+d)²-(a+b)²)
=(c-d-a+b)(c-d+a-b)(c+d+a+b)(c+d-a-b)
(2)原式=3(a²+6ab²+(3b²)²
=3(a+3b²)²
=(c²-b²+d²-a²+2(ab-cd))(c²-b²+d²-a²-2(ab-cd))
=((c-d)²-(a-b)²)((c+d)²-(a+b)²)
=(c-d-a+b)(c-d+a-b)(c+d+a+b)(c+d-a-b)
(2)原式=3(a²+6ab²+(3b²)²
=3(a+3b²)²
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原式=(c²-b²+d²-a²)²-[2(ab-cd)]²
=[(c²-b²+d²-a²)+2(ab-cd)][(c²-b²+d²-a²)-2(ab-cd)]
=[(c²+d²-2cd)-(b²+a²-2ab)][(c²+d²+2cd)-(b²+a²-2ab)]
=[(c-d)²-(a-b)²][(c+d)²-(a+b)²]
=[c-d+a-b][c-d-a+b][c+d+a+b][c+d-a-b]
=[(c²-b²+d²-a²)+2(ab-cd)][(c²-b²+d²-a²)-2(ab-cd)]
=[(c²+d²-2cd)-(b²+a²-2ab)][(c²+d²+2cd)-(b²+a²-2ab)]
=[(c-d)²-(a-b)²][(c+d)²-(a+b)²]
=[c-d+a-b][c-d-a+b][c+d+a+b][c+d-a-b]
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