计算(m-n-2q)^2 和 -3分之2(x-y)^2*4分之3(x-y)^4(x-y)3请问怎么写?
来源:学生作业帮 编辑:作业帮 分类:数学作业 时间:2024/08/28 05:39:22
计算(m-n-2q)^2 和 -3分之2(x-y)^2*4分之3(x-y)^4(x-y)3请问怎么写?
(m-n-2q)^2=(m-n)^2+4q^2-4q(m-n)=m^2+n^2-2mn+4q^2-4mq+4nq
-3分之2(x-y)^2*4分之3(x-y)^4(x-y)3=-2/3(x^2+y^2-2xy)*3/4(x^2+y^2-2xy)^2(x^2+y^2-2xy)(x-y)
=(x^2+y^2-2xy)(x^4+y^4+4x^2y^2+2x^2y^2-4x^3y-4xy^3)(x^3+xy^2-2x^2y-x^2y-y^3+2xy^2)
=(x^2 +y^2-2xy)(x^4+y^4+6x^2y^2-4x^3y-4xy^3)(x^3+3xy^2-3x^2y-y^3)
=(x^6+x^2y^4+6x^4y^2-4x^5y-4x^3y^3+x^4y^2+y^6+6x^2y^4-4x^3y^3-4xy^5-2x^5y-2xy^5-12x^3y^3+8x^4y^2-8x^2y^4)(x^3+3xy^2-3x^2y-y^3)
=(x^6+y^6-x^2y^4+15x^4y^2-6x^5y-20x^3y^3-6xy^5)(x^3+3xy^2-3x^2y-y^3)
=x^9+x^3y^6-x^5y^4+15x^7y^2-6x^8y-20x^6y^3-6x^4y^5+3x^8y^2+3xy^8-3x^3y^6+45x^5y^4-18x^6y^3-60x^4y^5-1x^2y^7-3x^8y-3x^2y^7+3x^4y^5-45x^6y^3+16x^7y^2+60x^5y^4+18x^3y^6-x^6y^3-y^9+x^2y^7-15x^4y^6-6x^5y^4-20x^3y^6+18xy^8
=x^9-y^9-4x^3y^6-98x^5y^4+31x^7y^2-9x^8y-84x^6y^3-78x^4y^5+21xy^8-3x^2y^7
-3分之2(x-y)^2*4分之3(x-y)^4(x-y)3=-2/3(x^2+y^2-2xy)*3/4(x^2+y^2-2xy)^2(x^2+y^2-2xy)(x-y)
=(x^2+y^2-2xy)(x^4+y^4+4x^2y^2+2x^2y^2-4x^3y-4xy^3)(x^3+xy^2-2x^2y-x^2y-y^3+2xy^2)
=(x^2 +y^2-2xy)(x^4+y^4+6x^2y^2-4x^3y-4xy^3)(x^3+3xy^2-3x^2y-y^3)
=(x^6+x^2y^4+6x^4y^2-4x^5y-4x^3y^3+x^4y^2+y^6+6x^2y^4-4x^3y^3-4xy^5-2x^5y-2xy^5-12x^3y^3+8x^4y^2-8x^2y^4)(x^3+3xy^2-3x^2y-y^3)
=(x^6+y^6-x^2y^4+15x^4y^2-6x^5y-20x^3y^3-6xy^5)(x^3+3xy^2-3x^2y-y^3)
=x^9+x^3y^6-x^5y^4+15x^7y^2-6x^8y-20x^6y^3-6x^4y^5+3x^8y^2+3xy^8-3x^3y^6+45x^5y^4-18x^6y^3-60x^4y^5-1x^2y^7-3x^8y-3x^2y^7+3x^4y^5-45x^6y^3+16x^7y^2+60x^5y^4+18x^3y^6-x^6y^3-y^9+x^2y^7-15x^4y^6-6x^5y^4-20x^3y^6+18xy^8
=x^9-y^9-4x^3y^6-98x^5y^4+31x^7y^2-9x^8y-84x^6y^3-78x^4y^5+21xy^8-3x^2y^7
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