When a problem is presented to us in writing, we can convert it into mathematical language (also called algebraic language) by transforming it into an algebraic expression. But what are algebraic expressions?

Variable: This is a letter that represents a numerical value, for example $X$ or $Y$. This letter refers to an unknown numerical value that we must work out. For example: if $X+5=8$, then we can conclude that the numerical value of $X$ is $3$.

An algebraic expression is a combination of numbers and letters (representing unknown numbers) that includes operations such as addition, subtraction, multiplication, division, etc.

Each element of an algebraic expression is called an algebraic term, be it a variable, a constant, or a combination of a coefficient and one or more variables. If the expression contains only one term, it is known as a monomial, while those that contain two or more terms are polynomials.

There is no limitation to the amount of constant numbers, unknown variables, or operations that can appear in an algebraic expression. In addition, there does not always have to be a variable in the algebraic expression, although it will always have a certain numerical value.

Let's take a look at some examples of algebraic expressions without variables:

$4+7$

$\frac{9}{3}$

$3-2$

$2\times8$

Here we can see that all of the expressions are composed of numbers and, since there are no unknown variables, we can calculate the result by simply performing the operations.

$4+7 =11$

$\frac{9}{3}=3$

$3-2=1$

$2\times8=16$

Now, let's look at some exampleswithvariables:

$X + 5$

$X-Y$

$A\times\frac{1}{2}$

$X^2+6$

In this case, the examples include numbers, unknown variables (represented by letters), and mathematical operations (addition, subtraction, multiplication, division, etc.).

Exercises: Variables in Algebraic Expressions

Exercise 1

Find the algebraic expression that corresponds to the number of squares in the nth figure.

Solution:

The first figure is formed from $1$ square.

The second figure is formed from $4$ squares, which can be expressed as $2$ by$2$.

The third figure is formed from $9$ squares, which can be represented as $3$ by$3$.

Following this pattern, we can work out that the nth figure will be formed from $n \times n = nĀ²$ squares.

Answer:

$nĀ²$

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How many exercises should I practice?

Since each student learns at a different pace, the answer to this question depends on you. The important thing is that you are aware of your level and therefore whether or not you need to practice the formulas more. That said, it is recommended that you do 10 basic and intermediate level exercises in order to learn a single basic formula.