When we get into the higher classes, algebra formulas are introduced to us. In algebra, we substitute numbers with letters or alphabets to get a solution. We use letters like (x, a, y, z, b, etc.) to represent unknown quantities in an equation, which are also known as variables. Then we solve the equation or algebra formula to get a definite answer. Algebra includes both numerals and letters. Numbers are fixed but their value is known in a given equation. In an algebra formula, unknown numbers or alphabets are used to represent a given form of equation. The combination of numbers, letters, factorials, matrices, etc. is used to form an equation or a formula. This is generally regarded as the methodology for algebra. In this article, we will try to understand some basic concepts regarding algebraic expressions and some important algebra formulas, and basic tips to remember them.
Algebraic Expression
The idea of expressing mathematical equations using numbers or alphabets without specifying their actual values is known as the algebraic expression. In our junior school, we learned how to use the basics of algebra using unknown values such as x, y, z, a, v, etc., which are also known as variables. In an algebraic equation, there are various terms such as constants, variables, coefficients. Let us take an example to have a clear point of view about these concepts. Suppose 5x-3 is an equation, here 5 is the coefficient of x and is well defined, 3 is the constant value that has a definite value and x is the variable having unknown value. If you want to learn about these concepts in detail and in a fun, effective, and interactive way, visit Cuemath.
Some Algebra Formulas
a.a – b.b = (a-b) (a+b)
(a+b) (a+b) = a.a + 2ab + b.b
(a-b) (a-b) = a.a – 2ab + b.b
a.a + b.b = (a-b) (a-b) + 2ab
(a+b+c) (a+b+c) = a.a + b.b + c.c + 2ab + 2ac + 2bc
(a-b-c) (a-b-c) = a.a + b.b + c.c – 2ab – 2ac + 2bc
a.a.a – b.b.b = (a-b) (a.a + ab + b.b)
a.a.a + b.b.b = (a+b) (a.a – ab + b.b)
(a+b) (a+b) (a+b) = a.a.a + 3a.ab + 3ab.b + b.b.b
(a-b) (a-b) (a-b) = a.a.a – 3a.ab + 3ab.b – b.b.b
Basic Tips to Remember Algebra Formulas
Algebra formulas are the cornerstone of most of the maths sum you solve. Thus, it is imperative that you learn and understand how to apply these formulas in the mathematical sums. You can memorize the algebra formulas by understanding how those formulas are derived. This will give you a two-fold benefit. Your problem-solving skills will improve, and continuous practice will help you retain various algebra formulas. You can also read out formulas loudly and then write it down repetitively a few times. This can help you in the retention of algebra formulas.
Types of Algebraic Expressions
There are basically three types of algebraic expressions which are as follows:
1. Monomial expression: Any algebraic expression which has only one term is known as monomial expression. For example, 3y, 11x, 8x, 8y, 9x, etc.
2. Binomial expression: Any algebraic expression which has two terms is known as binomial expression. For example, 8xy+8, x+ 9z, 5x + 6 etc.
3. Polynomial expression: An expression with more than one term and nonnegative integral exponents of a variable is known as polynomial expression. For example, ax + by + fa, 2x + 3q + 1z, etc.
Some Other Types of Algebraic Expressions
Other than monomial, binomial, polynomial types of expression, an algebraic expression can also be classified into other additional types which are as follows:
1. Numeric expression: A numeric expression does not have a variable but consists of numbers and operations. Some of the examples are as follows: 9 + 6, 45\5, etc.
2. Variable expression: A variable expression that consists of variables along with numbers and operations to define an expression is known as variable expression.