Multiplicative hyperrings as an significant type of algebraic hyperstructures extend rings such that the addition is an operation and the multiplication is a hyperoperation. In this paper, we aim to present and characterize two new classes of hyperideals in a commutative multiplicative hyperring called square-difference factor absorbing hyperideals and weakly square-difference factor absorbing hyperideals. We show that the class of square-difference factor absorbing hyperideals is a proper subclass of weakly square-difference factor absorbing hyperideals. We present a range of properties and characterizations for these notions, accompanied by relevant examples. Additionally, we examine the behavior of these classes of hyperideals under various hyperring constructions, including homomorphic images, quotient hyperrings, and cartesian product of multiplicative hyperrings.
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