Question

Factor completely 2x3y4 − 8x2y3 + 6xy2.

Answer 1

Answer:

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

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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:

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

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