(x^2+y^2)-4x^2y^2

来源：百度知道 编辑：UC知道 时间：2024/06/14 04:27:41
(1)x^2-16ax+64a^2; (2)5a^2(x-y)^3-30ab^2(y-x)^2;
(3)(x^2+y^2)-4x^2y^2; (4)a^-(b^2+c^2-2bc);
(5)x^2(x^2-y^2)+z^2(y^2-x^2); (6)(x+2)(x+4)+1.

需过程！在今晚11点前给出满意答案者，另奖20分！

(1)x^2-16ax+64a^2
直接完全平方
=(x-8a)^2

(2)5a^2(x-y)^3-30ab^2(y-x)^2;
=5a^2(x-y)^3-30ab^2(x-y)^2;
=5a(x-y)^2[a(x-y)-6b^2]
=5a(x-y)^2(ax-ay-6b^2)

(3)(x^2+y^2)^2-4x^2y^2
=(x^2+2xy+y^2)(x^2-2xy+y^2)
=(x+y)^2(x-y)^2

(4)a^2-(b^2+c^2-2bc)
=a^2-(b-c)^2
=(a+b-c)(a-b+c)

(5)x^2(x^2-y^2)+z^2(y^2-x^2)
=x^2(x^2-y^2)-z^2(x^2-y^2)
=(x^2-y^2)(x^2-z^2)
=(x+y)(x-y)(x+z)(x-z)

(6)(x+2)(x+4)+1.
=x^2+6x+8+1
=x^2+6x+9
=(x+3)^2

分少…没挑战性…费时