how linearizate the product of two continuous variables?

Question

I am building a mathematical model on cplex, using c++, and I would like linearizate the product of two continuous variables. I have the product of two continuous variables x * y in my objective function, where domain this variable are 0 <= x <= 1 and 0 <= y <= 1. Linearizate is to transform this product (x * y) into something that does not exist the multiplication of two variables.

Answer 1

$$(x+\Delta x)(y+\Delta y)=xy+x\Delta y+y\Delta x+\Delta x\Delta y$$

You linearize about some point $(x^*, y^*)$. And $$xy=x^*y^*+x^*\Delta y+y^*\Delta x$$