Algebra is the unifying thread of all mathematical topics. It is the study of mathematical symbols and the associated concepts that are used to manipulate them. The scope of algebra is very wide and can be used to perform simple arithmetic operations to solve complicated topics such as set theory, linear algebra, etc. Irrespective of the topic at hand, algebra formulas are the key to unlocking the answers to questions. In this article, we will see some basic formulas that are required, as well as go through the important topics covered under algebra.
Elementary Algebra
This type of algebra covers most of the traditional topics that are introduced to kids in secondary school. It includes performing arithmetic operations, evaluating equations, quadratic equations, logarithms and exponents, linear equations in one or two variables, formulation of common laws such as associativity, and so on. It is the most common form of algebra that is taught to kids and sees the systematic exploration of all properties of real numbers. Let us look at a sample of formulas and topics that come under elementary algebra.
1. Algebraic Identities
Identities are expressions that always hold true regardless of what value is assigned to a particular variable. Some identities that are taught to students are
- (a + b)2 = a2 + b2 + 2ac
- (a + b) (a – c) = a2 – b2
- (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
2. Algebraic Expressions and Equations
An algebraic expression is one that consists of variables, coefficients, constants and has basic arithmetic operations like +, -, *, and non-negative exponents. When two equations are equated using the equal sign, it forms an algebraic equation. Several manipulations can be done to such equations, one being their simplification.
- a2 + b2 = c2 (Also, known as the Pythagoras Theorem for right triangles)
- x2 – 10 = 6 is a conditional equation that is satisfied by only x = 4 and -4.
- m + n = n + m (This is the commutative property that holds true for all values)
3. Linear Equations in one or two variables
A linear equation derives its name from the fact that when they are plotted on a graph, it gives a straight line. The simplest equation has one variable, and more advanced equations consist of two variables. Examples are given below.
- One Variable : 2y + 16 = 20.
- Two Variables : 2y + 4x = 20; 2x – 4y = 40. These two equations can be solved to find x and y.
4. Exponents and Logarithms
An exponential equation is one in which numbers are expressed in the form of x n = a. Logarithms are another way to represent exponents. There are several algebraic formulas associated with exponents and logs. For example,
- x n = a. This is equivalent to log x a = n
- log a (xy) = log a (x) + log a (y)
5. Quadratic Equations
An equation that consists of a term with an exponent raised to 2 is known as a quadratic equation. Some of the operations performed on such equations are finding the value of the unknown variable or finding the roots of the equation.
Conclusion
There are several other topics such as matrices, vectors, functions, set theory, and so on that fall under the category of algebra and are introduced to kids in steps. To ensure that kids develop strong basics, they should avail themselves of the services of a reliable platform such as Cuemath. At Cuemath, the certified tutors believe in helping kids to develop a robust mathematical foundation that can not only be applied to the grade they are studying in but can help in building more complicated concepts. So start your journey in algebra with Cuemath today!
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