To factor the expression 16x² – 25, we can recognize that it is a difference of squares. The difference of squares follows the formula:
a² – b² = (a – b)(a + b)
In our case:
- a is 4x because (4x)² = 16x²
- b is 5 because 5² = 25
Now we can apply the difference of squares formula:
16x² – 25 = (4x)² – (5)² = (4x – 5)(4x + 5)
Thus, the complete factorization of the expression 16x² – 25 is:
(4x – 5)(4x + 5)