text: prove that the square of a number ending with5 =the product of the number excepting 5 and the number +1 then25 for example 75^2=7*8 followed by 25=5625 lets express the number we start with as x and y  x = the number before the 5 (e.g. 7) y always = 5  so to make 75, you have 10 * x + y ... (10*7)=70 + 5 = 75 if you square this equation you have (10x+y)^2   = 100x^2 + 10xy + 10xy + y^2 = 100x^2 + 20xy + y^2 = 100x^2 + 100x + y^2 ... (because y always = 5)  ---------  now we look at the other method.  product of number without the 5 is:  x(x+1) = x^2 + x  you're then putting 25 on the end. to do this, you're multiplying by 100 and adding y^2  100(x^2 + x) + y^2 = 100x^2 + 100x + y^2  there we have the same result as before.