Product of a Sum and a Difference (a + b)(a - b)
How to solve the product of a sum and a difference (a + b)(a - b): formula, 3 examples, and their solutions.
Formula
(a + b)(a - b) = a2 - b2
Factor the Difference of Two Squares: a2 - b2
Example(x + 2)(x - 2)
Solution
Solution (Detail)
(x + 2)(x - 2) = x2 - 22
22 = 4
So
x2 - 4
is the answer.
Example103⋅97
You can directly solve 103⋅97.
But let's solve this
by using the (a + b)(a - b) formula.
Solution
Solution (Detail)
Change 103 and 97
to a sum and a difference.
103*97 = (100 + 3)(100 - 3)
(100 + 3)(100 - 3) = 1002 - 32
1002 = 10000
32 = 9
10000 - 9 = 9991
So 9991 is the answer.
Example(x2 + 1)(x + 1)(x - 1)
Solution
Solution (Detail)
First solve (x + 1)(x - 1).
(x + 1)(x - 1) = (x2 - 12)
-12 = -1
(x2 + 1)(x2 - 1) = ((x2)2 - 12).
(x2)2
= x2⋅2
= x4
Power of a Power
-12 = -1
So
x4 - 1
is the answer.