因式分解：（1）x^3+xy^2-x^2y-y^3（2）x^2-x^y+xy^2-y^2(3)16a^4-B^4+4a^2-b^2_数学解答

因式分解：（1）x^3+xy^2-x^2y-y^3（2）x^2-x^y+xy^2-y^2(3)16a^4-B^4+4a^2-b^2

人气：341 ℃　时间：2020-05-13 20:34:03

解答

x^3+xy^2-x^2y-y^3
=x(x^2+y^2)-y(x^2+y^2)
=(x^2+y^2)(x-y)
x^2-x^2y+xy^2-y^2
=x^2-y^2-(x^2y-xy^2)
=(x+y)(x-y)-xy(x-y)
=(x-y)(x+y-xy)
16a^4-B^4+4a^2-b^2
=(4a^2-b^2)(4a^2+b^2)+(2a-b)(2a+b)
=(2a-b)(2a+b)(4a^2+b^2)+(2a-b)(2a+b)
=(2a-b)(2a+b)(4a^2+b^2+1)