Question

Factor completely 2x3y4 − 8x2y3 + 6xy2.

Answer 1

`2xy^2(xy-1)(xy-3)`

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Given expression

`2x^3y^4-8x^2y^3+6xy^2`

The greatest common factor of all three terms is
`2xy^2`.

Factor this out:

`2xy^2(x^2y^2-4xy+3)`

Complete the square:

`2xy^2(x^2y^2-4xy+4-1)=`

`2xy^2((xy-2)^2-1)`

Factorize further using the identity for the difference of squares:

`2xy^2(xy-2+1)(xy-2-1)=`

`2xy^2(xy-1)(xy-3)`