SOLUTION: Conjecture: The product of a number (x - 1) and the number (x + 1) is always equal to ____. 3*5 = 4^2-1 4*6 = 5^2-1 5*7 = 6^2-1 7*9 = 8^2-1 6*8 = 7^2-1 8*10 = 9^2-1 The

Algebra ->  Geometry-proofs -> SOLUTION: Conjecture: The product of a number (x - 1) and the number (x + 1) is always equal to ____. 3*5 = 4^2-1 4*6 = 5^2-1 5*7 = 6^2-1 7*9 = 8^2-1 6*8 = 7^2-1 8*10 = 9^2-1 The       Log On


   

Question 1091992: Conjecture: The product of a number (x - 1) and the number (x + 1) is always equal to ____.
3*5 = 4^2-1
4*6 = 5^2-1
5*7 = 6^2-1
7*9 = 8^2-1
6*8 = 7^2-1
8*10 = 9^2-1
The numbers above ^^ are for finding the conjecture.
Found 2 solutions by math_helper, ikleyn:
Answer by math_helper(2461) About Me  (Show Source):
You can put this solution on YOUR website!

You can use the numbers to see the pattern, but if you are in Algebra, you don't need to use numbers at all:
+%28x-1%29%2A%28x%2B1%29+=+x%5E2+%2B+x+-x+-+1+=+x%5E2+-1+
So +%28x-1%29%2A%28x%2B1%29+ is always equal to +highlight%28x%5E2+-+1%29+
—
Verify using x=8 (for example)
+%288-1%29%288%2B1%29+=+7%2A9+=+63++
and +8%5E2+-+1+=+64-1+=+63+ also.

Answer by ikleyn(52750) About Me  (Show Source):
You can put this solution on YOUR website!
.

The difference of squares formula is       a%5E2+-+b%5E2+=+%28a+%2B+b%29%2A%28a-+b%29.
      For details and examples of applications of this formula see the lesson The difference of squares formula in this site.



When I was a student, we learned it at the 6-th grade, I think, and I remember it all my life (as it should be).


I had good teachers. Thanks to them.