Question 535715
I would recognize the square of a binomial
{{{a^2+2ab+b^2=(a+b)^2}}} and
a difference of squares
{{{a^2-b^2=(a+b)(a-b)}}}
I would look for two monomials/terms that are perfect squares, such as
{{{4}}}, {{{81x^2}}}, {{{16x^4y^6}}}
If there is only two such monomials, and they have opposite signs, then I would see it as a difference of squares.
If there were two such monomials, with the same sign, and a third term, I would figure out if the third term is double the product of the square roots of the other two.
For example, in {{{36x-81x^2-4}}}
I recognize the perfect square terms {{{4}}}, and {{{81x^2}}}.
Since they both appear with a minus sign (same sign), I would calculate the square roots (of the monomials without the minus sign, of course), as
{{{2}}}, and {{{9x}}}.
Then I would calculate twice their product
{{{2(2)(9x)=36x}}}
Since it equals the third term, the factoring is
{{{36x-81x^2-4=(-1)(81x^2-36x+4)=(-1)(9x-2)^2}}}