Question 111596
=> these are the square of binomials: {{{(a+b)^2}}} and {{{(a-b)^2}}}

Important to know: 

If the binomial has a minus sign, then the minus sign appears {{{only}}}{{{ 

in}}}{{{ the}}}{{{ middle}}}{{{ term}}} of the trinomial.  

If the binomial is {{{a + b}}}, then the middle term will be {{{+2ab}}},  

and if the binomial is {{{a - b}}}, then the middle term will be {{{-2ab}}}; 

therefore, we can use the {{{double }}}{{{sign}}}  ("{{{plus_ or_ minus}}}"), 

to state the rule as follows:

{{{(a +- b)^2 = a^2 +- 2ab + b^2}}}

The square of {{{any }}}{{{binomial}}} produces the following three terms:


1.   The square of the first term of the binomial: {{{ a^2}}}

2.   Twice the product of the two terms:  {{{+-2ab}}}

3.   The square of the second term:  {{{b^2}}}


The square of {{{every}}}{{{ binomial}}}, called a perfect square trinomial, 

has that form:  {{{a^2 +- 2ab + b^2}}}.  

So, if your square your binomial {{{(b-c)^2}}}, it will be:
 
{{{ (b-c)^2 = b^2 -2bc + c^2}}}

{{{b^2}}} is the square of {{{b}}}.

{{{-2bc }}} is  twice the product of  {{{2b*(-c) = -2bc  }}}.  

{{{c^2}}} is the square of {{{-c}}}.