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The algebra we study in schools is called elementary algebra, that aims to impart the basic meaning to variables and constants. I still remember my first algebra class, when the arithmetic numbers were replaced by alphabets and I was dumbfounded looking at my teacher (duh!). Algebra is broadly classified into many branches. Some other branches of algebra, which are a part of mathematics and are studied at higher levels, are linear algebra, abstract algebra, vector spaces and ring and field theories etc. In elementary algebra, numbers are replaced by letters and symbols and with the help of these letters we solve the problems. For example, if we are asked to find the area of a rectangle (A), given its length (l) and breath (b), we all know its area will be:

Area of rectangle (A)= Length (l) X Breadth (b)

Now, if you know the value of either of the two quantities, among the three variables, we can substitute the value of the two known variables and get the third one! One of the simple algebra tips! Isn't it? We need algebra because it drastically reduces the space for problem solving and lengthy problems can be solved in a few lines. Algebra finds many applications in fields of engineering, finance, economics and architecture!

The mathematical problems in algebra are expressed through algebraic equations. Algebraic equations are a combination of variables and constants. For instance, consider the equation, 3X= 9. This is a simple algebraic equation in one variable. Dividing both sides by 3, we get the solution of this equation as, X=3. Similarly, 3X + 2Y = 8, is an algebraic equation in two variables. Now, since this equation has two variables, we will require another equation with the same variables, to find the solution of this equation. Now consider,

3X + 1Y - 7Z= 8

This is an example of a linear equation in three variables. X,Y and Z are the three variables in this equation. Let's check out some other simple algebra tips! Here in this equation. X, Y and Z are the three variables, whose values can change with the constraint that the left hand side (L.H.S) of the equation must always be equal to the right hand side (R.H.S) of the equation. The numbers 3, 1 and -7 are called the coefficients of X, Y and Z respectively. The respective values of X, Y and Z, which make the L.H.S=R.H.S are called solutions of the given algebraic expression. This is so, because if we take X=3, Y= -1 and Z=0 and put in the above equation, we would get L.H.S=R.H.S.! Try it! You will get 8=8. Its as simple as that! Here, we got the solution with the help of hit and trial method. Suppose, we had to find the solution of this equation algebraically, then we would require two other linear equations in three variables.

Some important algebra tips that are the basics of algebra are as follows

• We can add the same number on both sides of an equation. e.g., 5X - 8 = 7 is the same as 5X - 8 + 8 = 7 + 8.
• We can subtract the same number on both sides of an equation. e.g. 2a + 4 - 5 = 6 – 5.
• We can multiply both sides of an equation by the same (non-zero) number. e.g. (5/6)x = 7 is the same as 6 X (5/6)x = 7 X 6.
• We can divide both sides of an equation by the same (non-zero) number. e.g. 2r = 10 is the same as (2r/2) = (10/2).

Order Of Operations- The PEDMAS Rule

There is a famous and important rule of PEDMAS, that is crucial in solving algebra problems. An important algebra tip is to understand the order of operations, that means, the series of steps you need to take while solving a mathematics problem involving squares, brackets, addition, subtraction and others. So, what is BODMAS? While working out arithmetic calculations, follow the order of operations mentioned below.

P stands for parenthesis/brackets.
E stands for exponential (squares, exponents, cubes, square roots etc.)
DM stands for division and multiplication (performed left to right)
AS stands for addition and subtraction (performed left to right)

Let's understand the rule of PEMDAS through an example,

Example - Evaluate 9 - 4 ÷ (8 - 4) x 2 + 6 using the order of operations.

Solution
Step1. 9 - 4 ÷ (8 - 4) x 2 + 6 = 9 - 4 ÷ 4 x 2 + 6 (parenthesis)
Step2. 9 - 4 ÷ 4 x 2 + 6 = 9 – 1 x 2 + 6 (Division)
Step3. 9 – 1 x 2 + 6 = 9 – 2 + 6 (Multiplication)
Step4. 9 – (-2) + 6 = 9 +4 (Addition)
Step5. 9+4 = 13

Important Algebra Formulas or Algebra Tips

Some important formulas and algebraic tips are mentioned below:

Serial Number	Algebraic Formula
1	(a+b)2 = a2 + b2 + 2ab
2	(a - b)2 = a2 + b2 - 2ab
3	(a + b)3 = a3 + b3 + 3ab2 + 3a2b
4	a3 + b3 = (a + b)3 - 3a2b - 3ab2
5	(a-b)3 = a3- b3 - 3a2b + 3ab2
6	a3- b3 = (a - b)3 + 3ab(a+b)
7	(a + b + c)2 = a2 + b2 + c2 + 2(ab + bc + ca)
8	(a + b)2 + (a - b)2 = 2(a2 + b2)
9	(a2- b2) = (a - b)(a + b)
10	(a3 + b3) = (a + b)(a2 - ab+ b2)
11	(a3 - b3) = (a - b)(a2 + b2 + ab)

Learning algebra involves the understanding of the vital role of exponents and radicals. There are some major algebra tips, that can help solve various problems. Some of them are mentioned below:

Serial Number	Exponential Formula
1	anam = an+m
2	(a.b)n = an. bn
3	a0 = 1
4	(am)n = amn
5	am/n = n√am
6	a-m = 1/a-m
7	(am/an )= a(m-n)

Some Interesting Algebra Tricks

Algebra is a fantastic field that can present some interesting fallacies. Read one such trick,

Algebra Trick Question#1
Take some random number. Add 3 to this number and then multiply by 2. Again add 4 to the result and divide by 2. Now, subtract the number you started with from the result. What's the answer? Whoa! It's the same number!!Now, start with any other number and apply the same trick again, you will always get the number you started with. Let's see the proof of this trick using algebra tips. Here, I have taken my original number to be 'x'. It's fun!

Select a Number	Say x
Add 3	x+3
Multiply by 2	2(x+3) or 2x+6
Add 4	2x+10
Divide By 2	x+5
Subtract the original number	x

Likewise, there are many other algebra tricks that you can think on your own! All it takes is some interest to play with numbers and some knowledge of algebra. So, have fun studying algebra tips and algebra tricks!