Algebraic formulas play a very important role in solving aptitude questions related to various topics. It is estimated that 2-4 questions are always asked approximately in SSC exams from this section. The difficulty level of questions depends upon your adopted approach. Some questions consumes a lot of time in calculation because of their complexity.
In this article, we will learn about all algebraic formulas and their applications with shortcut tricks because all questions are based on algebraic formulas. Let us take a tour of it.
Algebra Formula
The Algebra formula is part of Class 10 in India. One of the most crucial areas of mathematics is algebra. Numerous disciplines, including quadratic equations, polynomials, coordinate geometry, calculus, trigonometry, probability, and others, can be solved using algebraic formulas. In Algebra formulas, we used numbers along with letters together. The most common letters used in algebraic equations and problems are X, Y, A, and B. These Algebra formulas enable us to quickly and efficiently tackle time-consuming algebraic problems. Here, we include all significant Algebra formulas together with their solutions, so that students can access them all in one place.
Algebra Formulas
Algebra formulas are basically algebra equations formed by algebraic and mathematical phrases and symbols. These algebraic formulas contain an unknown variable x which can be generated while simplifying an equation. These algebraic equations solve complicated algebraic computations in an easy way.
For Algebra formulas example,
(a+b)³ =a³+ 3a²b+3ab²+b³
In the above Algebra formulas, both sides are individually an algebraic equation. Where ( a³ + 3a²b+3ab²+b³ ) is the simplified expression of (a+b)³ .
Algebra formulas Square
Here are some Algebra formulas involving squares.
• 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 + 2bc + 2ca
• (a – b – c)² = a²+ b²+ c²– 2ab + 2bc – 2ca
Algebra formulas Cube for SSC CGL
Here are some Algebra formulas involving cubes.
• (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)(a²– ab + b²)
Some more Algebra formulas are –
• (a + b)⁴= a⁴+ 4a³b + 6a²b² + 4ab³ + b²
• (a – b)⁴= a4 – 4a³b + 6a²b² – 4ab³+ b⁴
• a⁴ – b⁴= (a – b)(a + b)(a² + b²)
• a⁵ – b⁵= (a – b)(a⁴ + a³b + a²b² + ab³+ b⁴)
Algebra formulas- Natural Numbers
Algebra formulas for Natural Numbers Except for 0 and negative numbers , the rest of the numbers [ 2 to infinity] in the number system that humans can count are known as Natural Numbrrs. Some algebraic formulas are applied when performing operations on natural numbers. They are.
Consider n to be a natural number.
- (an – bn )= (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
- ( an + bn)= (a + b)(an-1 – an-2b +…+ bn-2a – bn-1) [ where n is even , (n = k + 1) ]
- (an + bn )= (a + b)(an-1 – an-2b +an-3b2…- bn-2a + bn-1) [ where n is odd , (n = 2k + 1) ]
Algebraic Formulas- Laws of Exponents
In Algebra formulas An Exponent or power is used to demonstrate the repeated multiplication of a number. Such as 3×3×3×3 can be written as 3⁴ where 4 is the exponent of 3. In general, exponents or powers indicate how many times a number can be multiplied. There are various rules to operate an exponent for addition, subtraction, and multiplication which are easily solved by algebraic formulas.
Algebra Formulas- Quadric equations
Algebra formulas for Quadric equations are one of the most important topics in the syllabus of Class 9 and 10 . To find the root of the given quadric equations we used the following Algebra formulas
If ax²+bx+c =0 is a quadric equation ,then
From the above formula we can conclude that , If the roots of the quadric equation are α and β
1. The equation will be (x − α)(x − β) = 0,
2. The value of (α + β ) = (-b / a) and α × β = (c / a).
Algebra formulas For irrational Numbers (SSC CGL)
The Algebra formulas used to solve equations based on Irrational Numbers are following
- √ab = √a √b
- √a/b =√a / √b
- ( √a +√b ) ( √a – √b ) = a-b
- ( √a +√b )²= a + 2 √ab + b
- ( a +√b )( a -√b )= a² – b