把下列各式因式分解:(1)x2-9y2;(2)-64m2+81n2;(3)(2x+y)2-(x-2y)2;(4)169(
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把下列各式因式分解:
(1)x2-9y2;
(2)-64m2+81n2;
(3)(2x+y)2-(x-2y)2;
(4)169(a+b)2-121(a-b)2.
(1)x2-9y2;
(2)-64m2+81n2;
(3)(2x+y)2-(x-2y)2;
(4)169(a+b)2-121(a-b)2.
(1)x2-9y2
=(x+3y)(x-3y).
(2)-64m2+81n2
=81n2-64m2
=(9n+8m)(9n-8m).
(3)(2x+y)2-(x-2y)2
=[(2x+y)+(x-2y)][(2x+y)-(x-2y)]
=(3x-y)(x+3y).
(4)169(a+b)2-121(a-b)2
=[13(a+b)+11(a-b)][13(a+b)-11(a-b)]
=(24a+2b)(24b-2a).
=(x+3y)(x-3y).
(2)-64m2+81n2
=81n2-64m2
=(9n+8m)(9n-8m).
(3)(2x+y)2-(x-2y)2
=[(2x+y)+(x-2y)][(2x+y)-(x-2y)]
=(3x-y)(x+3y).
(4)169(a+b)2-121(a-b)2
=[13(a+b)+11(a-b)][13(a+b)-11(a-b)]
=(24a+2b)(24b-2a).
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