Home Education Algebra formula - Equations, Expressions, Examples

# Algebra formula – Equations, Expressions, Examples

Algebra formula : Algebra is one of the broad parts of mathematics, together with number theory, geometry and analysis. In its most general form, algebra is the study of mathematical symbols and the rules for manipulating these symbols; it is a unifying thread of almost all of mathematics. It includes everything from elementary equation solving to the study of abstractions such as groups, rings, and fields. The more basic parts of algebra are called elementary algebra; the more abstract parts are called abstract algebra or modern algebra. Elementary algebra is generally considered to be essential for any study of mathematics, science, or engineering, as well as such applications as medicine and economics. Abstract algebra is a major area in advanced mathematics, studied primarily by professional mathematicians.

Emergence Of Formal Equations

Perhaps the most basic notion in mathematics is the equation, a formal statement that two sides of a mathematical expression are equal—as in the simple equation x + 3 = 5—and that both sides of the equation can be simultaneously manipulated (by adding, dividing, taking roots, and so on to both sides) in order to “solve” the equation. Yet, as simple and natural as such a notion may appear today, its acceptance first required the development of numerous mathematical ideas, each of which took time to mature. In fact, it took until the late 16th century to consolidate the modern concept of an equation as a single mathematical entity.

• (a+b)²= a²+2ab+b²
• (a+b)²= (a-b)²+4ab
•  (a-b)²= a²-2ab+b²
•  (a-b)²= (a+b)²-4ab
•  a² + b²= (a+b)²-2ab.
•  a² + b²= (a-b)²+2ab.
•  a²-b²= (a +b)(a -b)
•  2(a²+b²)= (a+b)²+(a-b)²
•  4ab = (a+b)²-(a-b)²
•  ab = {(a+b)/2}²-{(a-b)/2}²
•  (a+b+c)² = a²+b²+c²+2(ab+bc+ca)
•  (a+b)³ = a³+3a²b+3ab²+b³
•  (a+b)³ = a³+b³+3ab(a+b)
•  a-b)³= a³-3a²b+3ab²-b³
•  (a-b)³= a³-b³-3ab(a-b)
•  a³+b³= (a+b) (a²-ab+b²)
•  a³+b³= (a+b)³-3ab(a+b)
•  a³-b³ = (a-b) (a²+ab+b²)
•  a³-b³ = (a-b)³+3ab(a-b)
• (a² + b² + c²) = (a + b + c)² – 2(ab + bc + ca)
•  2 (ab + bc + ca) = (a + b + c)² – (a² + b² + c²)
•  (a + b + c)³ = a³ + b³ + c³ + 3 (a + b) (b + c) (c + a)
•  a³ + b³ + c³ – 3abc =(a+b+c)(a² + b²+ c²–ab–bc– ca)
•  a3 + b3 + c3 – 3abc =½ (a+b+c) { (a–b)²+(b–c)²+(c–a)²}
• (x + a) (x + b) = x² + (a + b) x + ab
• (x + a) (x – b) = x² + (a – b) x – ab
•  (x – a) (x + b) = x² + (b – a) x – ab
•  (x – a) (x – b) = x² – (a + b) x + ab
•  (x+p) (x+q) (x+r) = x³ + (p+q+r) x² + (pq+qr+rp) x +pqr
•  bc (b-c) + ca (c- a) + ab (a – b) = – (b – c) (c- a) (a – b)
•  a² (b- c) + b² (c- a) + c² (a – b) = -(b-c) (c-a) (a – b)
• a (b² – c²) + b (c² – a²) + c (a² – b²) = (b – c) (c- a) (a – b)
•  a³ (b – c) + b³ (c-a) +c³ (a -b) =- (b-c) (c-a) (a – b)(a + b + c)
•  b²-c² (b²-c²) + c²a²(c²-a²)+a²b²(a²-b²)=-(b-c) (c-a) (a-b) (b+c) (c+a) (a+b)
•  (ab + bc+ca) (a+b+c) – abc = (a + b)(b + c) (c+a)
•  (b + c)(c + a)(a + b) + abc = (a + b +c) (ab + bc + ca)

## Basic Algebra

The algebra for class 6 covers all the basic concepts. Terms related to basic algebra skills are mentioned below.

1. Exponent
2. Expression
3. Polynomial (Monomial, binomial and trinomial)
4. Like terms and Unlike terms
5. Constants

An equation is a statement which implies two same identities separated by “=” sign. Whereas an expression is a group of different terms separated by ‘+’ or ‘-‘ sign.

Like terms are those terms whose variables and their exponents are same.

### Basic Algebra Rules

The basic algebra rules are mentioned below:

• The Symmetry rule
• The commutative rules
• Two rules for equation

### Basic Algebra Operations

The general arithmetic operations performed in the case of algebra are:

• Subtraction: x – y
• Multiplication: xy
• Division: x/y or x ÷ y

where x and y are the variables.

The order of these operations will follow the BODMAS rule, which means the terms inside the brackets are considered first. Then, roots and exponents are operated on second priority. Solve all the division and multiplication operations and later addition and subtraction.

### Basic Algebra Formula

The general formulas used in algebra to solve algebraic equations and find the values of unknown variables are given here:

• a2 – b2 = (a – b)(a + b)
• (a+b)2 = a2 + 2ab + b2
• a2 + b2 = (a – b)2 + 2ab
• (a – b)2 = a2 – 2ab + b2
• (a + b + c)2 = a2 + b2 + c2 + 2ab + 2ac + 2bc
• (a – b – c)2 = a2 + b2 + c2 – 2ab – 2ac + 2bc
• (a + b)3 = a3 + 3a2b + 3ab2 + b3
• (a – b)3 = a3 – 3a2b + 3ab2 – b3

These Algebra formula are used in higher secondary classes. Students can find algebra formulas for class 8, along with class 9, class 10, class 11 and class 12 here.