Factoring Products of Trinomials: 25 x^4 + 11 x^2 y^2 + 4 y^4

Dr Fua

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Dec 2, 2015
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I have been having difficulty with factoring products of trinomials. Can anyone suggest a systematic approach?

example:

. . . . .\(\displaystyle 25x^4\, +\, 11x^2y^2 + 4y^4\)

at first, i thought it was a product of two binomials, so i tried perfecting the square only to find it does not have any rational solutions....

my hypothesis is that, there might have been a term that has been canceled since it is alike. i just have no clue on a systematic way on tackling a problem like this.
 
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I have been having difficulty with factoring products of trinomials. Can anyone suggest a systematic approach?

example:

. . . . .\(\displaystyle 25x^4\, +\, 11x^2y^2 + 4y^4\)

at first, i thought it was a product of two binomials, so i tried perfecting the square only to find it does not have any rational solutions....

my hypothesis is that, there might have been a term that has been canceled since it is alike. i just have no clue on a systematic way on tackling a problem like this.

(5x2 + 2y2)2 - (3xy)2
 
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