Theory:

Variable:
A variable is a symbol that is undefined yet. A variable is something that keeps varying.

If '$$x$$' is a variable, $$x$$ can hold the value of any number.
Example:
If '$$x$$' denotes the age of a person, then $$x$$ can hold any value from $$1, 2, 3...$$ as age cannot be a negative number.

Co-efficient:
A co-efficient is a number used to multiply a variable.

The number multiplied read as being a co-efficient of a variable.
Example:
In $$5p$$, $$5$$ is the coefficient of '$$p$$'.

Constant:
A constant is any whole number such as $$0, 1, 2, 3,...$$

Expression:

We would have come across many expressions in mathematics such as $$3 + 2$$, $$6 - 4$$ and so on.

In algebra, such expressions are written using symbols.
An expression is a combination of variables and constants.

An algebraic expression can be both a combination of variables and constants or wholly variables.
Example:
$$2x$$ $$+$$ $$3$$, $$3x$$ $$+$$ $$4y$$ and so on.

Let us look at a few more expressions:

1. Consider $$4x + 10$$:

$$4$$ is the co-efficient of '$$x$$'.

$$x$$ is the variable.

$$10$$ is the constant.

$$4x + 10$$ is altogether an expression.

2. Consider $$7x + 2y$$.

$$7$$ is the co-efficient of '$$x$$'.

$$2$$ is the co-efficient of '$$y$$'.

'$$x$$' and '$$y$$' are variable $$1$$ and variable $$2$$ respectively.

$$7x + 2y$$ is altogether an expression.