Question

分解因式:(2x-3y)³+(3x-2y)³-125(x-y)³

Answer 1

(2x-3y)^3+(3x-2y)^3-125(x-y)^3
= (2x-3y)^3+(3x-2y)^3-(5x-5y)^3
= (2x-3y)^3+(3x-2y)^3-((2x-3y) +(3x-2y))^3

令m =2x-3y, n =3x-2y
上式
= m^3 +n^3 -(m+n)^3
= m^3 +n^3 -(m^3 +n^3 +3mn^2 +3m^2n)
= -3mn^2 -3m^2n
= -3mn(m+n) ....(将假设带入）
= -3(2x-3y)(3x-2y)((2x-3y)+(3x-2y))
= -3(2x-3y)(3x-2y)(5x-5y)
= -15(2x-3y)(3x-2y)(x-y)

追答

原式=(2x-3y+3x-2y)[(2x-3y)^2-(2x-3y)(3x-2y)+(3x-2y)^2]-(5x-5y)^3
=(5x-5y)(4x^2-12xy+9y^2-6x^2+4xy+9xy-6y^2+9x^2-12xy+4y^2)-(5x-5y)^3
=5(x-y)(7x^2-11xy+7y^2-25x^2+50xy-25y^2)
=5(x-y)(-18x^2+39xy-18y^2)
=15(y-x)(6x^2-13xy+6y^2)
=15(y-x)(2x-3y)(3x-2y)

Answer 2

波哦