Question

To square 75, one can multiply (70)(80) and add 25 to that product. Can someone explain how this would work, without calculating?

Answer 1

since a^2-b^2 = (a-b)(a+b)

a^2 = (a-b)(a+b)+b^2

75^2 = (75-5)(75+5)+5^2 = (70)(80)+25