Final answer:
The algebraic expression for the square of the sum of r and t is (r + t)², which expands to r² + 2rt + t².
Step-by-step explanation:
The student is asking for the algebraic form of the square of the sum of two variables, r and t. The algebraic expression for the square of the sum of r and t is written as (r + t)². When expanded, this expression is equivalent to r² + 2rt + t². This is derived from the general formula for the square of a binomial (a+b)² = a² + 2ab + b², where a and b are any two numbers or variables.
It's important to remember the order of operations and to make sure every term within the parentheses is squared, including the term that comes from the cross multiplication of r and t, which is 2rt.