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八年级数学解答题一般
题目
分解因式:
(1)5ax2+20axy+20ay2(1)5ax^{2}+20axy+20ay^{2}；
(2)(3x−4y)2−(4x+3y)2(2)\left(3x-4y\right)^{2}-\left(4x+3y\right)^{2}；
(3)(x2+25)2−100x2(3)(x^{2}+25)^{2}-100x^{2}；
(4)(x2−7)2+18(7−x2)+81(4)(x^{2}-7)^{2}+18(7-x^{2})+81.
知识点：运用公式法、十字相乘法章节：第12章 因式分解 / 12.2 因式分解的方法

答案与解析

答案

(1)5ax2+20axy+20ay2\left(1\right)5ax^{2}+20axy+20ay^{2}
=5a(x2+4xy+4y2)=5a(x^{2}+4xy+4y^{2})
=5a(x+2y)2=5a\left(x+2y\right)^{2}；
(2)(2)原式=(3x−4y+4x+3y)(3x−4y−4x−3y)=\left(3x-4y+4x+3y\right)\left(3x-4y-4x-3y\right)
=(7x−y)(−x−7y)=\left(7x-y\right)\left(-x-7y\right)
=−(7x−y)(x+7y)=-\left(7x-y\right)\left(x+7y\right)；
(3)(3)原式=(x2+25+10x)(x2+25−10x)=(x^{2}+25+10x)(x^{2}+25-10x)
=(x+5)2(x−5)2=\left(x+5\right)^{2}(x-5)^{2}；
(4)(4)原式=(x2−7−9)2=(x^{2}-7-9)^{2}
=(x2−16)2=(x^{2}-16)^{2}
=(x+4)2(x−4)2=\left(x+4\right)^{2}(x-4)^{2}.

解析

(1)5ax2+20axy+20ay2\left(1\right)5ax^{2}+20axy+20ay^{2}
=5a(x2+4xy+4y2)=5a(x^{2}+4xy+4y^{2})
=5a(x+2y)2=5a\left(x+2y\right)^{2}；
(2)(2)原式=(3x−4y+4x+3y)(3x−4y−4x−3y)=\left(3x-4y+4x+3y\right)\left(3x-4y-4x-3y\right)
=(7x−y)(−x−7y)=\left(7x-y\right)\left(-x-7y\right)
=−(7x−y)(x+7y)=-\left(7x-y\right)\left(x+7y\right)；
(3)(3)原式=(x2+25+10x)(x2+25−10x)=(x^{2}+25+10x)(x^{2}+25-10x)
=(x+5)2(x−5)2=\left(x+5\right)^{2}(x-5)^{2}；
(4)(4)原式=(x2−7−9)2=(x^{2}-7-9)^{2}
=(x2−16)2=(x^{2}-16)^{2}
=(x+4)2(x−4)2=\left(x+4\right)^{2}(x-4)^{2}.

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