First off, perfect squares are numbers that have factors that can be multiplied by two of the same numbers. (such as: 1,4,9,16,25,36,49,64,81, & 100). a perfect squares can also be when in is a number such as x^2 or x∧4 (as long as the exponents are multiples of two.) You might know that a binomial is two terms. So you can recognize it by those numbers I mentioned earlier being subtracted.
Hope you understood and I wasnt confusing =)