# Formula and derivation of a minus b whole square explained

Learn and know the formula of a minus b whole square in algebra. a minus b whole square is also called as an identity. This formula is one of the most important formula in algebra.

Along with the formula mentioning I have given derivation of (a-b) 2 formula also. We can derive the formula in two different methods. First method is from the regular process that is give below. The second method is from (a+b) 2 formula we can derive (a-b) 2 formula. For that what we need to do is in + sign you replace it with – sign.

## Derivation of a minus b whole square formula:

(a-b) 2 = (a-b) × (a-b)

= a× (a-b) – b× (a-b)

= a2 – ab –ab + b2

= a2 -2ab + b2

Therefore, (a-b) 2 = a2 -2ab + b2

a minus b whole square formula as follows:

a minus b whole square is equal to a square (a2) minus (-) product of 2, a and b plus (+) b square (b2)

i.e.  (a-b) 2 = a2 -2ab + b2

(a-b) 2 + 2ab = a2 + b2

Note:

a minus b whole square in terms of a plus b whole square formula.

(a-b) 2 = (a+b) 2 – 4ab

Example:

Find (a-b) 2 value if a = 7 and b = 3 by using the formula.

Solution:

We know that,

(a-b) 2 = a2 -2ab + b2

(a-b) 2 = 72 -2.7.3 + 32

(a-b) 2 = 49 – 42 + 9

(a-b) 2 = 58 – 42

(a-b) 2 = 16

Find a2 + b2 value if a-b = 3 and ab = 5.

Solution:

We know that

(a-b) 2 + 2ab = a2 + b2

(3)2 + 2. 5 = a2 + b2

9 + 10 = a2 + b2

19 = a2 + b2

Find (a-b) 2 value if a+b = 6 and ab = 2.

Solution:

We know that,

(a-b) 2 = (a+b) 2 – 4ab

(a-b) 2 = (6) 2 – 4.2

(a-b) 2 = 36 – 8

(a-b) 2 = 28