Besides mathematics, algebra is a vast area of mathematics that involves many interesting topics. Having a detailed understanding of algebra is very essential in many fields, apart from mathematics. Together with some knowledge about algebraic expressions and algebra formulas, you can refer to this article.
What is the algebraic expression?
Any variable that is treated with a mathematical operation like addition, subtraction, or multiplication, then we get an algebraic expression. In other words, an algebraic expression can be stated as a combination of different terms which are being operated on with different mathematical operations. Let us understand the concept of algebraic expression with the following examples:
2y+3, 8x-5, 9t/3, 3xy
Many different terms are involved in an algebraic expression. In the following section, we will gain a thorough understanding of the various concepts associated with an algebraic expression.
- Variable: A variable can be considered to be any symbol that does not have any fixed value assigned to it. For example, if we say x, then x can hold any value, such as 1, 2, …
- Constant: Any symbol that has a fixed value assigned to it can be considered constant. For example, 1,2…
In terms of variables and constants, we can say that an algebraic expression is an equation that has been formed by combining variables and constants.
What are the important formulas of algebraic expression?
Solving algebraic expressions is crucial to getting good marks in exams. But many complex algebra sums can be solved with the help of the basic formulas that are listed below.
- (a+b) = a^2+ 2ab + b^2
- (a-b) = a^2 – 2ab – b^2
- (a+b) (a-b) = a^2- b^2
What are the different types of algebraic expressions?
There are different types of algebraic expressions that are being listed below.
- Monomial: An equation that consists of one term with non-negative power can be considered a monomial algebraic expression.
- Binomial: An algebraic equation that consists of two terms can be considered a binomial algebraic expression.
- Trinomial: An algebraic expression that consists of exactly three terms is stated as a trinomial algebraic expression.
- Polynomial: An algebraic expression with a combination of one or more monomial expressions can be considered a polynomial algebraic expression.
- Multinomial: An algebraic expression that consists of more than one term is considered a multinomial algebraic expression.
Formulas of algebra
Many complex sums of polynomials, coordinate geometry, calculus, trigonometry, probability, and many more can be solved with the help of algebra formulas. Algebraic formulas play a very significant role in solving any complex sum in no time. But before going to the algebra formula, it is essential to have a detailed understanding of the concept of algebraic expression and the terms that are involved in the concept of algebraic expression.
- (a + b) ^2 = a^2 + 2ab + b^2
- (a – b)^2 = a^2 – 2ab + b^2
- (a + b)(a – b) = a^2 – b^2
- (a + b) ^3 = a^3 + 3a2b + 3ab2 + b^3
- (a – b)^3 = a^3 – 3a2b + 3ab2 – b^3
- a^3 + b^3 = (a + b) (a2 – ab + b2)
- a^3 – b^3 = (a – b) (a2 + ab + b2)
- (a + b + c) ^2 = a^2 + b^2 + c^2 + 2ab + 2bc + 2ca
It is critical to understand the concept of an algebraic expression precisely to simplify the algebraic expression. Because an algebraic expression can be solved only by simplifying the complex equation. However, to solve an algebraic expression, it is usually necessary to have a thorough understanding of each algebraic formula that will be required to solve the algebraic expression at a later stage. You can seek the advice of Cuemath if you want to gain a thorough understanding and vast knowledge of algebra. Professionals in Cuemath can guide anyone with efficiency and can solve any doubt about any question with accuracy. Hence, it would be an ideal decision to choose Cuemath as your guide if you want to score colorful marks in your mathematics exam.