Hey guys showing 1-1ness of an isomorphism (supposed) i reach asub1(x)+bsub1(x^2)=asub2(x)+bsub2(x2)

now according to my Linear Algebra book two polynomials like these are equal only if their respective coefficients are equal, but if we pick x to be say 2 the asub1 can be 2 and bsub1 can be 4, where as on the right side asub2 can be 4 bsub2 cab be 3, so the coefficients are not equal. Please help, thanks