It can be factored as the SQUARE OF A BINOMIAL
(a^2 - b^2) = (a - b)(a + b)
Each has two binomial factors.
The binomial usually has an x2 term and an x term, so we complete the square by adding a constant term. If the coefficient of x2 is not 1, we divide the binomial by that coefficient first (we can multiply the trinomial by it later). Then we divide the coefficient of x by 2 and square that. That is the constant that we need to add to get the perfect square trinomial. Then just multiply that trinomial by the original coefficient of x2.
Remember to factor out the GCF of the coefficients if there is one. A perfect square binomial will always follow the pattern a squared plus or minus 2ab plus b squared. If it's plus 2ab, that factors to (a + b)(a + b) If it's minus 2ab, that factors to (a - b)(a - b)
This is related to the fact that the square of both a positive and a negative number is always positive. The last term is simply the square of the second term, in the original binomial.
Yes. With w and z being any two numbers or variables: Take (w + z)2 = (w + z)(w + z) = ww + wz + zw + zz = w2 + 2wz + z2, which is the perfect square trinomial.
1. Factoring out a common monomial 2. Factoring out the differnece of two perfect square numbers 3. Factoring out a common binomial
200 is not a perfect square. Its square root is a fraction and the square root of a perfect square is always an integer.