The name alone creates a horrific image in the minds of the new starters of algebra. It is a branch of mathematics that deals with equations, expression, etc. It is quite a very vast subject; scientists have been studying algebra since the late 12th century and there is still a lot to find out even after hundreds of years. This makes up for the vastness of the subject, actually, algebra is quite a broad topic if we see it rhetorically. It usually involves the use of alphabets, Greek symbols, etc. There are also a lot of formulae to be learned. There is a wide range of applications of algebra in different mathematical topics. Let us see some of the topics below:
Calculus: Invented by Newton and Leibnitz in the 16th century, calculus is a topic of utmost importance. Its highly versatile nature and wide range of applications in different fields make its use inevitable. There is an extensive amount of algebra involved in calculus. Right from a simplification of expressions to expanding expressions, the very foundation of calculus highly depends upon the algebraic method of mathematics. One cannot think of solving or simplifying or proceeding in calculus without having a good grip on the topic of algebra, let alone the understanding of basic knowledge. So, it is quite apt to say that one needs to have a firm grip over algebra for dealing with calculus.
One who is proactive in the field of mathematics does not need to explain the uses and importance of the sacrosanct binomial theorem in mathematics. This topic has also a wide range of applications along with different topics and even subjects such as Physics, Chemistry, Statistics, etc. And to master or have a good grip over this topic one must have their knowledge of algebraic methods in mathematics intact and in place. The topic of algebraic methods also plays a crucial role in the foundation and pillars of binomials. Actually, binomial is nothing but an advanced form of algebra.
Faster calculation: The topic methods of algebra also help in significantly increasing the calculation speeds and the pace of simplification of expressions with numbers with exponents. Let us try to understand better with the help of an example. Suppose one has to find the square of 102. Now the basic method says for finding the square we multiply the same number by itself, but this would take an enormous amount of time. So we write 102 as (100+2) and instead do its square.
So we have (100+2)^2, this is of the form (a+b)^2= a^2+b^2+2ab. So (100 + 2)^2= (100)^2 + (2)^2 + 2×100×2= 10000 + 4 + 400= 10404. Finding the square of 100 is much easier than finding the square of 102, so this method is more desirable. Let us see one more example 97^2= (100 – 3)^2= (100)^2 + (3)^2 – 2 × 100 × 3= 10000 + 9 – 600= 9409. These methods are quite useful in the calculation of squares and cubes of the given numbers in a much more efficient way.
(a + b)2= a2 + b2+ 2ab
(a – b)2= a2 + b2– 2ab
a2 – b2= (a + b) (a – b)
(a + b)3= a3+ b3+ 3a2b + 3ab2
(a – b)3= a3 – b3 – 3a2b + 3ab2
These were some of the formulae which are widely used in mathematics and different topics. These are the very basic formulae which are required to be learnt in order to ensure that at least the concepts for basics must be crystal clear.
Studying and examining the facts and details mentioned above makes us familiar with the topic of algebra, its requirement, uses in different fields, sheer versatility etc. We came to know how important it is to have a good grip over algebraic methods and concepts in order to make sure that one does not lag in other topics as discussed above. It is also essential in increasing the calculation speeds.
If algebra is not your cup of tea, you can always rely on Cuemath to understand concepts and seeking expert help.