Math Doubts

${(a+b+c)}^2$ formula

Formula

${(a+b+c)}^2$ $=$ $a^2+b^2+c^2$ $+$ $2ab+2bc+2ca$

It is called $a+b+c$ whole square formula and read as $a$ plus $b$ plus $c$ whole square. It is mainly used to expand the square of sum of three terms in terms of them.

Proof

The $a+b+c$ whole square algebraic formula can be derived in two distinct mathematical approaches.

Algebraic Method

The expansion of $a+b+c$ whole square is derived in algebraic form by the multiplication of algebraic expressions.

Geometrical Method

On the basis of areas of square and rectangle, the $a$ plus $b$ plus $c$ whole square algebraic identity is derived in mathematical form geometrically.

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