To factor the expression 9x² + 25, we first recognize that this is a sum of squares. In algebra, a sum of squares cannot be factored into real numbers. However, if we consider factoring it over the complex numbers, we can utilize the formula for the sum of squares.
The expression can be rearranged as follows:
9x² + 25 = (3x)² + (5i)²
Here, we have rewritten 25 as (5i)², where ‘i’ represents the imaginary unit. Using the identity for factoring a sum of squares, we have:
(a² + b²) = (a + bi)(a – bi)
Applying that to our expression, we get:
9x² + 25 = (3x + 5i)(3x – 5i)
In conclusion, while you cannot factor 9x² + 25 into real linear factors, you can express it in terms of complex numbers as (3x + 5i)(3x – 5i).