Squaring a Difference
To find (a  b)^{2}, the square of a difference, we can use FOIL:
(a  b)(a  b) 
= a^{2}  ab  ab + b^{2} 

= a^{2}  2ab + b^{2} 
As in squaring a sum, it is simply better to remember the result of using FOIL.
To
square a difference, square the first term, subtract twice the product of the two
terms, and add the square of the last term.
Rule for the Square of a Difference
(a  b)^{2} = a^{2}  2ab + b^{2}
Example
Squaring a difference
Square each difference, using the new rule.
a) (x  6)^{2}
b) (3w  5y)^{2 }
c) (4  st)^{2 }
d) (3 5a^{3})^{2 }
Solution
a) (x  6)^{2} 
= x^{2}  2(x)(6) + 6^{2} 
For the middle term, subtract twice
the product: 2(x)(6). 

= x^{2}  12x + 6^{2} 
b) (3w  5y)^{2 } 
= (3w)^{2}  2(3w)(5y) + (5y)^{2} 

= 9w^{2}  30wy + 25y^{2} 
c) (4  st)^{2 } 
= (4)^{2 } 2(4)(st) + (st)^{2 } 

= 16 + 8st + s^{2}t^{2} 
d) (3 5a^{3})^{2 } 
= 3^{2}  2(3)(5a^{3}) + (5a^{3})^{2} 

= 9  30a^{3} + 25a^{6} 
