"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
