He **triple the square of a number** It is represented like this in algebraic language:

**3x²**

Three times a number is **3x**. The square of a number is **x².**

It can also be represented like this:

**3(x^2)**

In the same way, the square of a number is represented like this:

**x²**

And the **twice the square of a number** So:

**2x²**

**How to calculate triple the square of a number?**

He **triple the square of a number** is, in turn, another number, which is obtained by performing the operation of squaring it and then multiplying the result by 3.

For example: **triple the square of 2**.

the square of **2** is **4** and multiplying it by **3** is obtained **12**let’s see:

**3×22 = 3×4 = 12**

Another example: **triple the square of 3**.

The resulting operation is:

**3×32 = 3×9 = 27**

**Three times the square of a negative number**

The number can be negative, in which case there is no problem with the sign, since the square of any number is always a positive quantity.

For example: **three times the square of −2.**

The same result is obtained as if the number were 2:

**3×(−2)2 = 3×4 = 12**

The operation is also valid if it is a fractional number or a decimal number, as will be seen in the examples later.

**Use of algebraic language in the ****triple the square of a negative number**

Three times the square of a number can be written **using algebraic language**.

The algebraic language uses letters like the **x** to represent quantities that are unknown or that can assume any value. Therefore, any «number» is represented as X, regardless of the value it has.

The X is the most used letter in these cases, although any other will do. As we speak of the «triple of the square of a number», the **x** it must be squared, which is indicated by the exponent **«2»** which is written above, on the right:

*The square of a number:* x2

Then, to indicate that the square of the number is multiplied by **«3»**this value is placed before it, writing it to the left side, and it remains:

*Three times the square of a number:* 3×2

This is a good example of *algebraic expression*.

Another way to write the «triple of the square of a number» is by the following product:

**3 ∙ x ∙ x**

So, it is valid to write:

**3×2 = 3 ∙ x ∙ x**

**The numerical value of an algebraic expression**

As stated, X can take any value.

When a certain value of X is substituted and the operation is carried out, a quantity is obtained, which is called *numerical value* of the algebraic expression.

Initially we found the numerical values of 3×2 when x = 2, x = 3, and x = −2.

It was also said that **x** it is not limited to integer values only, but to any number, as seen in the examples given below.

**worked examples**

**Example 1**

Find the numerical value of 3×2 in the following cases:

a) x = 10

b) x = ½

c) x = 0.5

**Solution to**

3×102 = 3×100 = 300

**solution b**

3× ½2 = 3×(1/4)= ¾

**solution c**

3×0.52 = 3×0.25 = 0.75

**Example 2**

Write the following expressions in algebraic language:

a) One added to three times the square of a number

b) Three times the square of a number decreased by 2

c) A number plus three times the square of the number minus 7

**Solution to**

To the number 1 is added (added) triple the square of a number, which is 3×2, and it is obtained:

1 + 3×2

It is also equivalent:

3×2+1

Since the commutative property is fulfilled: the order of the addends does not alter the sum.

**solution b**

2 is subtracted from 3×2, and it is necessary to respect the order, since the subtraction is not commutative:

3×2 – 2

**solution c**

In this case, any «number» is represented by «x», 3×2 is added to said number and then 7 is subtracted:

x + 3×2 – 7

Normally the expression is written, in equivalent form, ordering the powers from greatest to least:

3×2 +x – 7