Question

factorice 2x³-4xy²+2y³

Answer 1

2x³-4xy+2y³=2(x³-2xy²+2y³)

Answer 2

Answer:

2 ( x - y ) ( x² + xy - y² )

Step-by-step explanation:

Putting x = y gives

2x³ - 4x³ + 2x³ = 0

so (x-y) is a factor [by the Factor Theorem].

It is also easy to see that 2 is a common factor of the terms.

So we look for a factorization of the form

2x³ - 4xy² + 2y³ = 2 ( x - y ) ( ax² + bxy + cy² ).

Expanding the right and equating coefficients gives:

Coefficient of x³:  2 = 2a  =>  a = 1

Coefficient of x²y:  0 = 2b - 2a  =>  b = a = 1

Coefficient of y³:  2 = -2c  =>  c = -1

Therefore the factorization is

2x³ - 4xy² + 2y³ = 2 ( x - y ) ( x² + xy - y² ).