To add like terms in an algebraic expression, we can simply combine the coefficients of the terms with the same variable(s). In this case, we can combine the terms with x and the terms with y:

14x + 3y + 25x + 2y

= (14x + 25x) + (3y + 2y) (grouping like terms)

= 39x + 5y

Therefore, the value of 14x+3y+25x+2y is 39x + 5y.