Factorise x^2+y^2
the "sum of squares" does not factor over the set of real numbers.
To factorize the expression x^2 + y^2, we need to determine if it can be written as a product of two or more simpler expressions. However, x^2 + y^2 cannot be factored further using real numbers.
The expression x^2 + y^2 represents a sum of squares. It is a special case of the binomial formula known as the sum of squares formula or Pythagorean identity.
The Pythagorean identity states that when two variables, x and y, are squared and added together, the result can be represented in the following form:
x^2 + y^2 = (x + y)(x - y)
So while we cannot factorize x^2 + y^2 further using real or rational numbers, we can write it in the form (x + y)(x - y).
Hence, the complete factorization of x^2 + y^2 is (x + y)(x - y).