因式分解4x²(x-y)+(y-x)

问题描述:

因式分解4x²(x-y)+(y-x)

原式=(x-y)(4x²-1)=(x-y)(2x+1)(2x-1)

4X^4+Y^4=(2X^2+Y^2)(2X^2-Y^2) 4X^4+Y^4=4X^4+Y^4+4x^2y^2 - 4x^2y^2=(2x^2+y^2)^2 - 4x^2y^2 =(2x^2+y^2

4x²(x-y)+(y-x)=(x-y)(4x²-1)=(x-y)(2x-1)(2x+1)

4x²(x-y)+(y-x)
=(x-y)(4x²-1)
=(x-y)(2x+1)(2x-1)

(x-y)(2x-1)(2x+1)

4x²(x-y)+(y-x)
=(4x²-1)(x-y)
=(2x-1)(2x+1)(x-y)

4x²(x-y)+(y-x)
=4x²(x-y)-(x-y)
=(x-y)(4x²-1)
=(x-y)(2x+1)(2x-1)

4x²(x-y)+(y-x)
=4x²(x-y)-(x-y)
=(4x²-1)(x-y)
=(2x+1)(2x-1)(x-y)