Proof Of Algebra Formula

proof-

(a+b)²=a²+2ab+b²

LHS=(a+b)²

=(a+b)(a+b)

=a(a+b)+b(a+b)

=a²+ab+ab+b²

=a²+2ab+b² proved

(a-b)²=a²-2ab+b²

LHS=(a-b)²

=(a-b)(a-b)

=a(a-b)-b(a-b)

=a²-ab-ab+b²

=a²-2ab+b² proved

(a²-b²)=(a+b)(a-b)

=(a+b)(a-b)

=a(a-b)+b(a-b)

=a²-ab+ab-b²

=a²+(ab-ab)-b² (यंहा +ab और -ab कट के जीरो हो जायेगा)

=a²-b² proved 

a²+b²=(a+b)²-2ab or (a-b)²+2ab

LHS-a²+b²

=a²+2ab-2ab+b²

=a²+2ab+b²-2ab(यंहाa²+2ab+b²=(a+b)²)

=(a+b)²-2ab proved

or

=a²-2ab+b²+2ab{यंहा a²-2ab+b²=(a-b)²

=(a-b)²+2ab proved

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