Proved that :- (a+b)^2 = a^2+2ab+b^2

Welcome to my article Proved that :- (a+b)^2 = a^2+2ab+b^2. This question is taken from the simplification lesson.
The solution of this question has been explained in a very simple way by a well-known teacher by doing addition, subtraction, and fractions.
For complete information on how to solve this question Proved that :- (a+b)^2 = a^2+2ab+b^2, read and understand it carefully till the end.

Let us know how to solve this question Proved that :- (a+b)^2 = a^2+2ab+b^2

First write the question on the page of the notebook.

Proved that :- (a+b)^2 = a^2+2ab+b^2

LEFT HAND SIDE

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

We can also write \displaystyle {{\left( {a+b} \right)}^{2}} as (a+b )(a+b).

\displaystyle \left( {a+b} \right)\left( {a+b} \right)

\displaystyle a\left( {a+b} \right)+b\left( {a+b} \right)

\displaystyle a\times a+a\times b+b\times a+b\times b

\displaystyle {{a}^{2}}+ab+ba+{{b}^{2}}

\displaystyle {{a}^{2}}+ab+ab+{{b}^{2}}

\displaystyle {{a}^{2}}+2ab+{{b}^{2}}

Thus

left hand side = right hand side

\displaystyle {{a}^{2}}+2ab+{{b}^{2}} = \displaystyle {{a}^{2}}+2ab+{{b}^{2}} (proved)

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