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

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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
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

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
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)

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