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# Squaring a Difference

To find (a - b)2, the square of a difference, we can use FOIL:

 (a - b)(a - b) = a2 - ab - ab + b2 = a2 - 2ab + b2

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 = a2 - 2ab + b2

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 -5a3)2

Solution

 a) (x - 6)2 = x2 - 2(x)(6) + 62 For the middle term, subtract twice the product: 2(x)(6). = x2 - 12x + 62
 b) (3w - 5y)2 = (3w)2 - 2(3w)(5y) + (5y)2 = 9w2 - 30wy + 25y2
 c) (-4 - st)2 = (-4)2 - 2(-4)(st) + (st)2 = 16 + 8st + s2t2
 d) (3 -5a3)2 = 32 - 2(3)(5a3) + (5a3)2 = 9 - 30a3 + 25a6