 Quandaries and Queries Can you explain the steps for me, that get you from (a - b)2  to a2 - 2ab + b2 Thanks John Hi John, This follows from what is called "the distributive property of multiplication over addition". The property is just this 2 (3 + 5) = 2 8 =16 but there is another way to evaluate this expression, you can distribute the multiplication over the addition and then add. What I mean is 2 (3 + 5) = 2 3 + 2 5 = 6 + 10 = 16 The distributive property is that a (b + c) = a b + a c This distribution also is valid if the multiplication is on the right (a + b) c = a c + b c Now let's look at your problem (a - b)2 = (a - b) (a - b) I want to see the first "(a - b)" as one quantity and call it x, and I also want to see the second "(a - b)" as (a + (-b)). The expression is then (a - b)2 = (a - b) (a - b) = x (a + (-1)b) The distributive property then says that this is x a + x (-1)b = x a - x b = (a - b) a - (a - b) b Now use the distributive property on the right (again seeing (a - b) as (a + (-1)b). (a - b) a - (a - b) b = a a - a b - (a b - b b) = a2 - ab - (ab - b2) = a2 - 2 ab - b2 Penny Go to Math Central