问题 解答题
计算下列各题:
(1)(-4x-3y2)(3y2-4x);
(2)(3a2+
1
2
b)(3a2-
1
2
b)(9a4-
1
4
b2
(3)a(a-b)2-2b(a-b)(a+b);
(4)(a2-ab+b2)(a2+ab+b2
答案

(1)(-4x-3y2)(3y2-4x),

=(-4x)2-(3y22

=16x2-9y4

(2)(3a2+

1
2
b)(3a2-
1
2
b)(9a4-
1
4
b2),

=[(3a22-(

1
2
b)2](9a4-
1
4
b2),

=(9a4-

1
4
b22

=81a8-

9
2
a4b2+
1
16
b4

(3)a(a-b)2-2b(a-b)(a+b),

=a(a2-2ab+b2)-2b(a2-b2),

=a3-2a2b+ab2-2a2b+2b3

=a3-4a2b+ab2+2b3

(4)(a2-ab+b2)(a2+ab+b2),

=[(a2+b22]-(ab)2

=a4+a2b2+b4

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