Concept:Binomial: It is a type of polynomial that contains only two terms. It is the simplest kind of polynomial after the monomials (contains only one term).Degree of a polynomial: It is the highest power of the variable of its individual terms.Formula used: (a + b)2 = a2 + 2ab + b2(a - b)2 = a2 - 2ab + b2a2 - b2 = (a + b)(a - b)Calculation:Let's check from the option, one by one.(1) (x5 - 1)2 - (x5 + 1)2 + 5x5? x10 - 2x5.1 + 1 - (x10 + 2x5.1 + 1) - 5x5= x10 - 2x5 + 1 - x10 - 2x5 - 1 - 5x5= 5x5 Which is monomial with degree 5.(2) (x5 + 1)2 + (x5 - 1)2= x10 + 2x5.1 + 1 + x10 - 2x5.1 + 1= 2x10 + 2Which is binomial with degree 10.(3) (x5 + 1)2 + (x5 - 1)2 -2(x10 - x5)= x10 + 2x5.1 + 1 + x10 - 2x5.1 + 1 - 2x10 + 2x5= 2x5 + 2 Which is binomial with degree 5.(4) (x5 - 1) (x5 + 1)= x10 - 1Which is binomial with degree 10.Hence, from the above discussion, we can see that only option 3 is correct.