Question

求一数学题解 分解因式：（x^2+xy+y^2)^2-2xy(x^2+xy+y^2)-3x^2y^2

Answer 1

=（x²+xy+y²)²－2xy（x²+xy+y²)+x²y²－x²y²－3x²y²
=（x²+xy+y²－x²y²）²－4x²y²
=（x²+xy+y²－x²y²－2xy）（x²+xy+y²－x²y²+2xy）
=（x²+y²－x²y²－xy）（x²+y²－x²y²+3xy)

Answer 2

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