por 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 12let’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