Final answer:
The expression (8a^3 - 98a) is equivalent to the factored forms 2a(4a^2 - 49) and the further factored form 2a(2a+7)(2a-7), as a result of factoring out the common factor and recognizing the difference of squares.
Step-by-step explanation:
The expression (8a^3 - 98a) can be factored by looking for common factors in both terms. The common factor here is 2a, which leads us to the equivalent expression 2a(4a^2 - 49).
This is because 2a multiplied by 4a^2 gives you 8a^3, and 2a multiplied by -49 gives you -98a. Factoring further, we recognize that (4a^2 - 49) is a difference of squares and can be factored to (2a+7)(2a-7).
Therefore, 2a(2a+7)(2a-7) is also an equivalent expression to the original one. When simplifying expressions in algebra, it is crucial to eliminate terms wherever possible and check the answer to see if it is reasonable.