Final answer:
The value of 'a' in the factored form of the expression 144x²-1, which is (12x-1)(12x+a), is equal to 1.
Step-by-step explanation:
The expression 144x²-1 can be factored using the difference of squares formula, which is ² - b² = (a + b)(a - b). The expression can be thought of as (12x)² - (1)². To find the value of a, we can compare the constant terms in the factored form with those in the given expression.
The constant term in the factored form is -1. Therefore, we have: Thus, when factored, it becomes (12x + 1)(12x - 1). To match the student's given format of (12x - 1)(12x + a), we can see that a equals 1.