How to write a program in C to do operations on algebraic expression containing 2 variables?

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C

Matrix

How can I add or subtract 2 Algebraic expressions in C which have 2 variables. I realize it could be done using matrix but that would leave many null spaces. Can anyone please write a program dynamically allocating the arrays. How can I do with sparse matrix (array representation)
Example question:
P1(x,y) = 5x^2y + 9x^3y^2
P2(x,y) = 9x^3y^2 + 12y^2 + 10x^4

What I have tried:

I have tried to do it normally using matrix in C but my professor discarded it as it was creating too much unnecessary memory