An ‘Identity’ is a term in maths where the left hand side and the right hand side of that specific equation are always the same irrespective of what values you use to verify it. These two identities are (a + b) 2 = a2 + 2ab + b2 and (a – b) 2 = a2 - 2ab + b2. You can use any of these formulae to find the square.
Let us find the square of 52. However, before starting off, let us determine when to use (a + b) 2 and when (a – b) 2. To be concise indetermining this, there is a shortcut. For numbers which end in 1, 2, 3 and 4 it is advisable to use (a + b) 2. For numbers which end in 6, 7, 8 and 9 it is advisable to use (a – b) 2.
Now, coming back to our example of 52, we have to first divide the number into two such numbers whose sumwill be 52 and one of the numbers will be in the table of 10. Such a pair of two numbers will be 50 and 2 (50 + 2 = 52).
(50 + 2) 2 = 502 + 2 X 50 X 2 + 22 – this is what we will get as the expansion of the identity. As the mathematics rules tell us, the number with an index is always solved first. So, 2500 (the square of 50) and 4 (the square of 2) will be the first two results.
The result of 2 X 50 X 2 will be (should be) solved in the third step, which is 200. In the next step, add 2500, 200 and 4. The result you get will be 2704. So, that is the square of 52.
Using this formula, which is in fact an identity, you can find the square of any number. I hope, this illustration is sufficient for you to figure out how to find the square of any number with this formula.
With this, you will get an idea of how you can use (a – b) 2. With a little logic and common sense, you can easily use (a – b) 2 as well.