${(a+b+c)}^2$ $=$ $a^2+b^2+c^2$ $+$ $2ab+2bc+2ca$
The a plus b plus c whole square formula is derived in algebraic form by geometrical approach as per the areas of square and rectangle.
The square whose area is $a$ plus $b$ plus $c$ whole square, is divided as three squares and six rectangles.
The area of whole square is ${(a+b+c)}^2$ geometrically.
The whole square is split as three squares and six rectangles. So, the area of whole square is equal to the sum of the areas of three squares and six rectangles.
${(a+b+c)}^2$ $\,=\,$ $a^2+ab+ca$ $+$ $ab+b^2+bc$ $+$ $ca+bc+c^2$
Now, simplify the expansion of the $a+b+c$ whole square formula to obtain its expansion in simplified form.
Thus, the expansion of a plus b plus c whole square is proved in algebraic form by the geometrical approach in mathematics.
$\,\,\, \therefore \,\,\,\,\,\, {(a+b+c)}^2$ $\,=\,$ $a^2+b^2+c^2$ $+$ $2ab+2bc+2ca$
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