Question: How to use factor elementwise?

Hi Guys,

It might be a very basic question, but I am struggling with it for a quite a time.  I have an expression in a form of


and I want to use factor operation elementwise, i.e., it can individually act on h(x) and can give me

f(x)=h1(x)*h2(x)+g1(x)*g2(x). But whenever I am putting factor operation with elementwise it is not giving me desired answer. It would be really helpful and great if someone can help me out.

I am attaching maple sheet for reference also.

Thanks in advance and regards



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