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.

\[3x -5\]

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** $1$

## Expert Answer

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$.

## Numerical Results

The **t****ranslation **of “$91$ more than the **square** of a number” into an algebraic **equation** is:

\[ y = x^2+91 \]

## Example

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:

\[ y = x^3+53 \]