Question

(2x+y)³-(x-2y)³因式分解 -4x³y+16x²y²-16xy³

Answer 1

(2x+y)³-(x-2y)³
=((2x+y)-(x-2y))((2x+y)^2-(2x+y)(x-2y)-(x-2y)^2)
=(2x+y-x+2y)(4x^2+4xy+y^2-2x^2+4xy-xy+2y^2-x^2+4xy+4y^2)
=(x+3y)(x^2+11xy+7y^2)
因式分解 -4x³y+16x²y²-16xy³
=-4xy(x^2-4xy+4y^2)
=-4xy(x-2y)^2

Answer 2

(2x+y)³-(x-2y)³
=(2x+y-x+2y)[(2x+y)²+(2x+y)(x-2y)+(x-2y)²]
=(x+3y)(4x²+4xy+y²+2x²-3xy-2y²+x²-4xy+4y²)
=(x+3y)(7x²-3xy-3y²)

-4x³y+16x²y²-16xy³
=-4xy(x²-4xy+4y²)
=-4xy(x-2y)²

Answer 3

原式=【2x+y-x+2y][(2x+y)²+（2x+y)（x-2y)+（x-2y)²]
=（x+3y)(4x²+4xy+y²+2x²-3xy-2y²+x²-4xy+4y²)
=（x+3y)(7x²-3xy+3y²)
原式=-4xy(x²-4xy+4y²)=-4xy（x-2y)²