Question

(2x-3y)^3 +(3x-2y)^3-125(x-y)^3 这个怎么因式分解

RT

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)

Answer 2

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 3

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Answer 4

(2x-3y)³ +(3x-2y)³-125(x-y)³
=[(2x-3y)+(3x-2y)][(2x-3y)²-(2x-3y)(3x-2y)+(3x-2y)²]-125(x-y)³
=5(x-y)(4x²-12xy+9y²-6x²+13xy-6y²+9x²-12xy+4y²)-125(x-y)³
=5(x-y)[7x²-11xy+7y²-25(x-y)²]
=-5(x-y)(18x²-39xy+18y²)
= -15(x-y)(2x-3y)(3x-2y)

Answer 5

(2x-3y)^3 +(3x-2y)^3 - (5x-5y)^3
=(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 -25x^2 +50xy - 25y^2)
=5(x-y)(-18x^2 +39xy -18y^2)
=-15(x-y)(6x^2 - 13xy + 6y^2)
-15(x-y)(2x-3y)(3x-2y)