Question

to find (a+b)2 = a^2+2ab+ b^2 with algorithm ​

Answer 1

(a+b)²=a²+b²+2ab............(1)

proof

Take an example:(5+10)²

According to equation (1)

(5+10)²=(5)²+(10)²+2(5)(10)

LHS

(5+10)²

=(15)²

=225

RHS

(5)²+(10)²+2(5)(10)

=25+100+100

=125+100

=225

LHS=RHS

Hence, proved.

Answer 2

(a+b)^2 = a^2 + 2ab + b^2

This is an algebraic identity, to proof this


(a+b)^2 can be written as (a+b) (a+b)

Now open the bracket and multiply the terms
, you will get the equation as : a (a+b) + b (a+b)

Now open the bracket and multiply the terms

You will get a^2 + ab +ba +b^2

Now by multiplicative identity we know that a*b =b*a (*= multiplication)

There fore : a^2 + ab +ba +b^2 = a^2 + 2ba +b^2