Algebra is a branch of Mathematics that substitutes letters for numbers. An algebraic equation depicts a scale, what is done on one side of the scale with a number is also done to either side of the scale.
In almost every field of study, from computer science to engineering, algebra is immensely important. So, learners must grasp every algebra formula to prepare themselves for calculations beyond basic math. Not only for learners in school but even candidates appearing for competitive exams should have a firm grasp of algebraic formulae to excel.
Important Formulas in Algebra
Here is a list of Algebraic formulas –
- (a+b)2 = a2 + 2ab + b2
- (a – b)2 = a2 – 2ab + b2
- a2 – b2 = (a – b)(a + b)
- a2 + b2 = (a – b)2 + 2ab
- (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 + b3 + 3ab(a + b)
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- a3 – b3 = (a – b)(a2 + ab + b2)
- a3 + b3 = (a + b)(a2 – ab + b2)
- (a + b)3 = a3 + 3a2b + 3ab2 + b3
- (a – b)3 = a3 – 3a2b + 3ab2 – b3
- (a + b)4 = a4 + 4a3b + 6a2b2 + 4ab3 + b4)
- (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)
- If n is a natural number, an – bn = (a – b)(an-1 + an-2b+…+ bn-2a + bn-1)
- If n is even (n = 2k), an + bn = (a + b)(an-1 – an-2b +…+ bn-2a – bn-1)
- If n is odd (n = 2k + 1), an + bn = (a + b)(an-1 – an-2b +…- bn-2a + bn-1)
- (a + b + c + …)2 = a2 + b2 + c2 + … + 2(ab + ac + bc + ….
- Laws of Exponents (am)(an) = am+n (ab)m = ambm (am)n = amn
- Fractional Exponents a0 = 1
Do you know?
- Algebra was introduced by the Greeks back in the 3rd century.
- It was the Babylonians who created the algebraic equation and formulae we still use in the 21st century to solve diverse problems.
- Modern algebra was brought in by Rene Descartes in the 16th century.
Here’s what is involved in the study of algebra
The study of algebra revolves around in-depth learning of terms, concepts and formulae. The idea is simple. Here, mathematical symbols, known as variables, represent quantity without having any fixed value and these are manipulated to derive solutions.
A basic example:
Algebra asks questions like what is the value of x if x + 15 = 20? To get the result, you need to do another calculation, i.e. 20 – 15 = 5. So, the value of x is 5.
Once you learn the basics (elementary algebra), advanced levels gradually become easier.
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