a+b+c whole square formula explained with derivation

Learn and know the a+b+c whole square formula. As it consists of three terms, it is a trinomial. We can also say we are learning the formula for square of trinomial. In algebra, this is one of the special formulas that we should learn.

Learning the a+b+c whole square formula along with its derivation is good. In case when you forget formula, derivation process if you know then you can derive and write the formula easily. So I recommend remembering formula as well as remembering derivation is useful.

Derivation of a+b+c whole square formula:

${ \left( a+b+c \right) }^{ 2 }$

= (a+b+c) × (a+b+c)

= a × (a+b+c) + b × (a+b+c) + c × (a+b+c)

= ${ a }^{ 2 }$ + a×b + a×c + b×a + ${ b }^{ 2 }$ + b×c + c×a + c×b + ${ c }^{ 2 }$

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2×a×b + 2×b×c + 2×c×a

(or)

= ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2 × (a×b + b×c + c×a)

Therefore, ${ \left( a+b+c \right) }^{ 2 }$ = ${ a }^{ 2 }$ + ${ b }^{ 2 }$ + ${ c }^{ 2 }$ + 2× (a×b + b×c + c×a)

Hope you learnt a+b+c whole square formula with derivation.