Learn and know **a+b whole square** formula which is the one of the important formulas in the algebra chapter. On this formula we can prepare a mathematics model also.

In mathematics, where ever we are getting formulas, it is good to learn them and know how the formula is obtained. This will make you to understand the formula very well. Now we will learn what is **a+b whole square** formula and how this formula is obtained. After this we will try to know whether **a+b whole square formula** is considered as an identity or not.

**Derivation of a+b whole square formula:**

**a+b whole square** mathematically, we can write as { \left( a+b \right) }^{ 2 } .

{ \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 }

Finally we got { \left( a+b \right) }^{ 2 } = { a }^{ 2 } +2ab+ { b }^{ 2 }

**The formula of (a+b) whole square as follows:**

The derivation of **(a+b) whole square** is clearly given step by step in the above topic. At the ending of derivation we got the result, that’s the formula for { \left( a+b \right) }^{ 2 } .

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

**Can we say { \left( a+b \right) }^{ 2 } as an identity?**

In algebra, we have so many identities in that identities can we say that { \left( a+b \right) }^{ 2 } is one of the identity? To decide this i.e. whether it is identity or not, first you have to know what is an identity?

Yes, we say { \left( a+b \right) }^{ 2 } ** formula as an identity.**

**Some other formulas obtained from (a+b)**^{2} formula:

^{2}formula:

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

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

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

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

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

Example:

Expand { \left( 2x+3y \right) }^{ 2 }

Solution:

The given problem is in the form of { \left( a+b \right) }^{ 2 } **.**

We know that,

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

{ \left( 2x+3y \right) }^{ 2 } = { \left( 2x \right) }^{ 2 } + 2 × 2*x* × 3*y* + { \left( 3y \right) }^{ 2 } = 4 { x }^{ 2 } + 12xy + 9 { y }^{ 2 }

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