For any three consecutive numbers, prove algebraically that the largest number and the smallest number are factors of the number that is one less than the square of the middle number.

"For any three consecutive numbers": x,y,z:
x
y=x+1
z=x+2

"prove algebraically that the largest number and the smallest number are factors"
x*z=

"of the number that is one less than the square of the middle number"

=y²-1

x*z=y²-1
x*(x+2)=(x+1)²-1
x²+2x=x²+2x+1-1
x²+2x=x²+2x

both sides of the equation are the same, so the statement is correct