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.

a+b+c whole square formula explained

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.

Also Read:

a plus b whole cube formula

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