Question

What are algebraic expressions?

Answer 1

Hint: In this question, we have to find out the definition of algebraic expression.
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number).

Complete step-by-step answer:
In this question, we have to evaluate the definition of algebraic expressions.
In mathematics, an algebraic expression is an expression built up from integer constants, variables, and algebraic operations (addition, subtraction, multiplication, division, and exponentiation by an exponent that is a rational number) and to simplify algebraic expressions we will consider the highest power first then less the powers accordingly and end it with the constant term..
For example,
\[2\left( {x - 4} \right)\]is an algebraic expression.
Since taking the square root is the same as raising to the power \[\dfrac{1}{2}\],
\[\sqrt {\dfrac{{1 - {x^2}}}{{1 + {x^2}}}} \]is also an algebraic expression.
By contrast, transcendental numbers like \[\pi \]and e are not algebraic, since they are not derived from integer constants and algebraic operations. Usually, Pi is constructed as a geometric relationship and the definition of e requires an infinite number of algebraic operations.

Note: Algebraic operation:
In mathematics, a basic algebraic operation is any one of the common operations of arithmetic, which include addition, subtraction, multiplication, division, raising to an integer power, and taking roots (fractional power).
To simplify algebraic expressions we will consider the highest power first then less the powers accordingly and end it with the constant term.
“Operations” mean things like add, subtract, multiply, divide, squaring, etc. If it isn’t a number it is probably an operation.
You need to always follow the BODMAS rule. Calculate them in the wrong order, and you can get a wrong answer.