Algebraic expression can be defined as expression which is comprised of constants (values that cannot be changed), variables (values that can be changed as required), and a finite number of algebraic operations such as addition, subtraction, multiplication, and power (exponential) etc. In other words, an algebraic expression can be stated as expression which has signs and symbols of algebraic mathematics. Symbols may involve Numbers, signs of operation (+, -, *, / etc). Algebraic expression shows one number or one quantity as a result. For instance, sum of 3 and 6 is expressed as 3 + 6 in algebraic form and its result is only one quantity, that is, 9.
Algebraic expressions may contain more numbers of symbols along with brackets. Proper way of simplifying algebraic expressions is to solve the large bracket first and then small brackets and then addition, subtraction, multiplication and finally division symbol. Various terms and coefficients are used in algebraic expressions. Terms of an algebraic expression are those parts which are connected by plus and minus signs. Coefficients are constant along with variables. For instance, consider an algebraic expressions 3 p q x + r y – c. here 3 p q x, r y, and c are terms of expression. Let's take an example to know how simplifying algebraic expression is possible.
(10 – 3) * 5 + (5 * 3) 2x + 3y – 25 + 4x = (7) * 5 + (15) 2x + 3y – 25 + 4x,
= 35 + 30x + 3y – 25 + 4x,
= 35 - 25 + 30x + 4x + 3y,
= 10 + 34x +3y,
Rearranging, (10 – 3) * 5 + (5 * 3) 2x + 3y – 25 + 4x = 34x + 3y + 10.