When as students we started learning mathematics, it was all about numbers. Natural numbers, whole numbers, integrals. Then we started learning about mathematical functions like addition, subtraction, BODMAS and so on. And then suddenly from class 8 onwards or so, mathematics had alphabets and letters! And so our introduction to algebra began. Today, we will focus on algebra and algebra formula. Let’s get started!
Introduction to Algebra
Mathematics is a vast field. It is impossible for one person to know everything there is to know in mathematics, even after a lifetime of study. And while it can be cumbersome, mathematics is also one of the most important fields of study. Right from how much to tip the waiter to when the universe began, all answers can be found due to the application of maths.
As we approach the higher classes, we see our introduction to algebra. In algebra, we substitute numbers with letters or alphabets to arrive at a solution. We use these letters like (x, a, b etc.) to represent unknown quantities in an equation. Then we solve the equation or algebra formula to arrive at a definite answer.
Algebra itself is divided into two major fields. The more basic functions that we learn in school are known as elementary algebra. Then the more advanced algebra formula, which is more abstract in nature fall under modern algebra, sometimes even known as abstract algebra.
Algebra includes both numbers and letters. Numbers are fixed, i.e. their value is known. Letters or alphabets are used to represent the unknown quantities in the algebra formula. Now, a combination of numbers, letters, factorials, matrices etc. is used to form an equation or formula. This is essentially the methodology for algebra.
As students study for their exams, there are certain very important algebra formulas and equations that they must learn. These formulas are the cornerstone of basic or elementary algebra. Only learning the formulas is not sufficient. The students must also understand the concept behind the formula and learn to apply them correctly.
Here, we will provide a list of all the important algebra formulas. The comprehensive list will allow the students to have a quick look before exams or refer to whenever they wish. Remember, only rote learning is not enough. You must also know how to effectively apply these formulas to a problem.
- a² – b² = (a-b)(a+b)
- (a+b)² = a² + 2ab + b²
- (a-b)² = a² – 2ab + b²
- 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
- 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
- “n” is a natural number, an – bn = (a-b) (an-1 + an-2b +….bn-2a + bn-1)
- “n” is a even number, an + bn = (a+b) (an-1 – an-2b +….+ bn-2a – bn-1)
- “n” is an odd number an + bn = (a-b) (an-1 – an-2b +…. – bn-2a + bn-1)
- (am)(an) = am+n (ab)m = amn
Q: Find the value of 17² – 4²
Ans: Now these are simple numbers, so we can calculate the answer. But the correct method is to apply the formula,
a² – b² = (a-b)(a+b)
17² – 4² = (17-4)(17+4) = 13 × 21 = 273