How do you write an algebraic expression of “product of $9$ and t squared increased by the sum of square of t and \[2\]” ? 

Hint: In the given question, we are required to write an algebraic expression based on the information given to us. First, break down the information given to us to try and identify what algebraic expression must look like. You should always know what you are dealing with. A sum means that you are adding something, so you are going to use the $ + $ sign.

Complete step by step solution:
The “product of $9$ and t squared” means first squaring the variable t and then multiplying the square of t with $9$.
So, the algebraic expression for the above statement is $9{t^2}$.
This product of $9$ and t squared is then increased by the sum of square of t and \[2\]. So, the algebraic expression is: $9{t^2} + {(t + 2)^2}$.
Additional Information: When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combinations of mathematical symbols is called a mathematical expression. 
Note:  An expression is a sentence with a minimum of two numbers and at least one math operation. This math operation can be addition, subtraction, multiplication, and division.
A math expression is different from a math equation. An equation will always use an equivalent $\left( = \right)$ operator between the two terms. It is not a surprise that variables act like pronouns, because math is basically its own language, defined by numeric and logical rules.