Square of a Binomial
To square a binomial, multiply the binomial by itself:
(a + b)^{2} = (a + b)(a + b)
(a + b)^{2}  =  (a + b)(a + b) 

 =  a^{2} + ab + ba + b^{2} 

 =  a^{2} + ab + ab + b^{2} 

 =  a^{2} +2ab + b^{2} 

The square of a binomial is always the sum of:
 The first term squared,

2 times the product of the first and second terms, and
 the second term squared.
When a binomial is squared, the resulting trinomial is called a perfect square
trinomial.
Examples:
(x + 5)^{2} = x^{2} +2(x)(5) + 5^{2} = x^{2} + 10x + 25
(100  1)^{2} = 100^{2} +2(100)( 1) + ( 1)^{2} = 10000  200 + 1 = 9801
(2x  3y)^{2} = (2x)^{2} +2(2x)( 3y) + ( 3y)^{2} = 4x^{2} 12xy + 9y^{2}
Product of the Sum and Difference of Two Terms
When we multiply two polynomials that are the sum and difference of
the same 2 terms  (x + 5) and (x  5) for example  we get an
interesting result:
(a + b)(a  b)  =  a(a) + a( b) + ba + b( b) 

 =  a^{2}  ab + ab  b^{2} 

 =  a^{2}  b^{2} 

The product of the sum and difference of the same two terms is always
the difference of two squares; it is the first term squared minus the
second term squared. Thus, this resulting binomial is called a
difference of squares.
Examples:
(7  2)(7 + 2) = 7^{2} 2^{2} = 49  4 = 45
(x + 9)(x  9) = x^{2} 9^{2} = x^{2}  81
(2x  y)(2x + y) = (2x)^{2}  y^{2} = 4x^{2}  y^{2}
(3x^{2} 2)(3x^{2} +2) = (3x^{2})^{2} 2^{2} = 9x^{4}  4
( y + 5x)( y  5x) = ( y)^{2}  (5x)^{2} = y^{2} 15x^{2}