This question belongs to the pure algebra domain and aims to explain the algebraic expressions, how to form algebraic equations, and squared numbers.
Algebraic expressions are the opinion of expressing numbers utilizing letters or alphabets without prescribing their true values. The root concepts of algebra guide us on how to represent an unrevealed value by utilizing the letters such as $x, y, z$, etc. These letters are named here as variables.
Both variables and constants can be a mixture of an algebraic term. The coefficient is a term used when any value is put before and multiplied by a variable. An algebraic term in mathematics is an indication that is made up of variables and constants, along with algebraic operations (subtraction, addition, etc.). Expressions are made up of terms. Algebraic expressions are defined with the assistance of unspecified constants, variables, and coefficients.
The mixture of these three (as terms) is stated as an expression. It is to be mentioned that, unlike the algebraic equation, an algebraic expression has no equal to the $=$ sign.
In the above algebraic expression, x is a variable, whose value is unspecified to us and it can take any value. $3$ is comprehended as the coefficient of $x$, as it is a constant value employed with the variable term and is well described. $5$ is the constant value term that has an actual value. A square number or perfect square in mathematics is an integer that is the square of an integer, Also, it is the multiplication of some integer with itself. For instance, 4 is a square number, since it equals $$^2$ and can be denoted as $4 \times 4$.
The typical notation for the square of a numeral $n$ is not the product $n \times n$, but the identical exponentiation $n^2$, normally enunciated as “n squared“. The term square number comes from the word shape. The unit area is described as $(1 \times 1)$. Therefore, area $n^2$ means a square with side length $n$. If a square number is described by $n$ points, the points can be placed in rows as a square per side, which has the exact numeral points as the square root of $n$. Therefore, square numbers are a kind of figurate numbers. The square-free term is used for a positive integer that has no square divisors except $1$
Assume the number is $x$.
The Square of a number is $x^2$.
$91$ more than the square of a number will be the $ x^2 + 91$.
The translation of “$91$ more than the square of a number” into an algebraic equation is:
\[ y = x^2+91 \]
Write an algebraic expression for 53 more than the cube of a number.
Let the number be $x$.
The cube of a number is $x^3$.
$53$ more than the square of a number will be $x^3 + 53$.
“$53$ more than the cube of a number” into an algebraic equation is:
\[ y = x^3+53 \]