text: Lets express the number we start with as x and y\n\nx = the number before the 5 (e.g. 7)\ny always = 5\n\nSo to make 75, you have 10 * x + y ... (10*7)=70 + 5 = 75\nIf you square this equation you have (10x+y)^2 \n\n= 100x^2 + 10xy + 10xy + y^2\n= 100x^2 + 20xy + y^2\n= 100x^2 + 100x + y^2 ... (because y always = 5)\n\n---------\n\nNow we look at the other method.\n\nProduct of number without the 5 is:\n\nx(x+1) = x^2 + x\n\nYou're then putting 25 on the end. To do this, you're multiplying by 100 and adding y^2\n\n100(x^2 + x) + y^2\n= 100x^2 + 100x + y^2\n\nThere we have the same result as before.