1. kmullis6

Directions: Complete the conjecture based on the pattern you observe in the specific cases. Conjecture: The product of a number (n - 1) and the number (n +1) is always equal to _____. $3\times5=4^{2}-1$ $4\times6=5^{2}-1$ $5\times7=5^{2}-1$ $6\times8=7^{2}-1$ $7\times9=8^{2}-1$ $8\times10=9^{2}-1$

2. misty1212

HI!!

3. misty1212

it is not clear? what do you think $9\times 11$would equal in that pattern?

4. kmullis6

99 so odd number. that's the types of questions i'm answering right now.

5. misty1212

lets look more carefully

6. misty1212

the right hand side of each equal sign is some number squared minus 1 right?

7. kmullis6

Yes

8. misty1212

and that number, the number being squared, is half way between the other two numbers right?

9. misty1212

the number in the middle of $$n-1$$ and $$n+1$$ is just $$n$$

10. misty1212

so what they are showing you, by example instead of by algebra, is that $(n-1)(n+1)=n^2-1$

11. kmullis6

12. misty1212

lol no, the answer is $$n^2-1$$

13. kmullis6

oohhhh ok. sorry haha :P thank you (: