To factor the expression x² + 10x + 25 completely, we start by looking for patterns or using methods like grouping or the quadratic formula.
This expression is a perfect square trinomial. The structure follows the general form:
a² + 2ab + b² = (a + b)²
Here, we can identify:
- a = x
- b = 5
Now, substituting these values into the pattern:
(x + 5)²
Therefore, the complete factorization of the expression x² + 10x + 25 is:
(x + 5)(x + 5) or simply (x + 5)².
This means the quadratic can be expressed as the square of a binomial, confirming that the factors of the expression are identical, which can be useful when solving equations or graphing.