Step-by-step explanation:
To prove the identity we just manually compute the left hand side of it, simplify it and check that we do get the right hand side of it:
[tex](a+b)^2=(a+b)\cdot(a+b)[/tex] (that's the definition of squaring a number)
[tex]=a\cdot a + a\cdot b + b \cdot a +b \cdot b[/tex] (we distribute the product)
[tex]=a^2+ab+ba+b^2[/tex] (we just use square notation instead for the first and last term)
[tex]=a^2+ab+ab+b^2[/tex] (since product is commutative, so that ab=ba)
[tex]=a^2+2ab+b^2[/tex] (we just grouped the two terms ab into a single term)
