Please help, I'll give fan & medal

Question

kmullis6 · Answer

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 _____.

$$3\times5=4^{2}-1$$
$$4\times6=5^{2}-1$$
$$5\times7=5^{2}-1$$
$$6\times8=7^{2}-1$$
$$7\times9=8^{2}-1$$
$$8\times10=9^{2}-1$$

misty1212 · Answer

HI!!

misty1212 · Answer

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

kmullis6 · Answer

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

misty1212 · Answer

lets look more carefully

misty1212 · Answer

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

kmullis6 · Answer

Yes

misty1212 · Answer

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

misty1212 · Answer

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

misty1212 · Answer

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

kmullis6 · Answer

so the answer is n?

misty1212 · Answer

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

kmullis6 · Answer

oohhhh ok. sorry haha :P thank you (: