Final answer:
The expression 49x^(2)-25 is factored as (7x + 5)(7x - 5), which is the result of applying the difference of squares formula a^2 - b^2 = (a + b)(a - b).
Step-by-step explanation:
To factor the expression 49x^(2)-25, we recognize it as a difference of squares. Since both 49 and 25 are perfect squares, we can rewrite this expression as (7x)^2 - 5^2. The difference of squares can be factored using the formula a^2 - b^2 = (a + b)(a - b).
Therefore, the factored form of the expression is:
(7x + 5)(7x - 5)
Remember that when you raise each expression inside parentheses to a power, the power affects everything inside the parentheses including the number. This concept is similar to when we raise whole expressions to an integer power. For instance, (2x)^2 = 2^2 * x^2. Thus, it's clear we apply the exponents to both the coefficient and the variable.