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将下列多项式分解因式 (1)4x^3y-16xy^3 (2)2-2分之一a^2(3)(3x-y)^2-(x+3y)^2(4)a^4-16b^4
(1)4x^3y-16xy^3 (2)2-2分之一a^2(3)(3x-y)^2-(x+3y)^2(4)a^4-16b^4
人气:425 ℃ 时间:2020-04-23 09:36:04
解答
(1)4x^3y-16xy^3
=4xy(x^2-4y^2)
=4xy(x-2y)(x+2y)
(2)2-2分之一a^2
=1/2(4-a^2)
=1/2(2-a)(2+a)
(3)(3x-y)^2-(x+3y)^2
=(3x-y+x+3y)(3x-y-x-3y)
=(4x+2y)(2x-4y)
=4(2x+y)(x-2y)
(4)a^4-16b^4
=(a^2+4b^2)(a^2-4b^2)
=(a^2+4b^2)(a+2b)(a-2b)
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