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 { \left( a-b \right) }^{ 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 ** { \left( a+b \right) }^{ 2 } **formula we can **derive { \left( a-b \right) }^{ 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:**

** { \left( a-b \right) }^{ 2 } ** = (a-b) × (a-b)

= a× (a-b) – b× (a-b)

= { a }^{ 2 } – ab –ab + { b }^{ 2 }

= { a }^{ 2 } -2ab + { b }^{ 2 }

Therefore, ** { \left( a-b \right) }^{ 2 } ** = { a }^{ 2 } -2ab + { b }^{ 2 }

**a minus b whole square formula as follows:**

**a minus b whole square** is equal to a square ( { a }^{ 2 } ) minus (-) product of 2, a and b plus (+) b square ( { b }^{ 2 } )

i.e. ** { \left( a-b \right) }^{ 2 } ** = { a }^{ 2 } -2ab + { b }^{ 2 }

** { \left( a-b \right) }^{ 2 } **+ 2ab = { a }^{ 2 } + { b }^{ 2 }

Note:

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

** { \left( a-b \right) }^{ 2 } ** = ** { \left( a+b \right) }^{ 2 } ** – 4ab

Example:

♦ **Find { \left( a-b \right) }^{ 2 } value if a = 7 and b = 3 by using the formula.**

Solution:

We know that,

** { \left( a-b \right) }^{ 2 } ** = { a }^{ 2 } -2ab + { b }^{ 2 }

** { \left( a-b \right) }^{ 2 } ** = { 7 }^{ 2 } -2.7.3 + { 3 }^{ 2 }

** { \left( a-b \right) }^{ 2 } ** = 49 – 42 + 9

** { \left( a-b \right) }^{ 2 } ** = 58 – 42

** { \left( a-b \right) }^{ 2 } ** = 16

♦ **Find { a }^{ 2 } + { b }^{ 2 } value if a-b = 3 and ab = 5.**

Solution:

We know that

** { \left( a-b \right) }^{ 2 } **+ 2ab = { a }^{ 2 } + { b }^{ 2 }

{ 3 }^{ 2 } + 2. 5 = { a }^{ 2 } + { b }^{ 2 }

9 + 10 = { a }^{ 2 } + { b }^{ 2 }

19 = { a }^{ 2 } + { b }^{ 2 }

♦ **Find { \left( a-b \right) }^{ 2 } value if a+b = 6 and ab = 2.**

Solution:

We know that,

** { \left( a-b \right) }^{ 2 } ** = ** { \left( a+b \right) }^{ 2 } ** – 4ab

** { \left( a-b \right) }^{ 2 } ** = { 6 }^{ 2 } – 4.2

** { \left( a-b \right) }^{ 2 } ** = 36 – 8

** { \left( a-b \right) }^{ 2 } ** = 28

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