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 |
|