Look for the 1-2-1 pattern, a trinomial with squares where the 1's are and a central product multiplied by 2. Example: 4x^2+20xy+25y^2=(2x+5)^2. The middle term is 2*2*5, that is, 2 times the product of 2x and 5y.
Another example is 9x^2-6x+1=(3x-1)^2. The central term has minus but the other terms are just the same as above regarding the sign. The minus tells you that we have (3x-1) instead of (3x+1).
Difference of squares: There is no middle term and the other two terms are perfect squares.
Example: 16-9y^2=(4-3y)(4+3y).