The first and last terms of the trinomial must be perfect squares.
The square roots of these, when multiplied together and doubled, must equal the value of the middle term.
If this is all true, then you can write the answer in one step;
Use the square roots, make two identical binomials, each with the sign of the middle term.
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Example:
4x2 - 12xy + 9y2
[First & last terms have square roots 2x and 3y
These multiply to 6xy, doubled is 12xy]
= (2x - 3y) (2x - 3y)
= (2x - 3y)2
Both negative since the middle term of the polynomial was negative.
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