![\"post4pic1\"](\"http:\/\/advancedmathyoungstudents.com\/blog\/wp-content\/uploads\/2014\/03\/post4pic1.jpg\")
<\/a><\/p>\nWe can find its area by subtracting the little square from the big one to get:<\/p>\n
Area = x2<\/sup> \u2013 y2<\/sup><\/i><\/strong><\/p>\n But we can also find the area another way.\u00a0 Let’s cut things up and move them around.<\/p>\n As you can see, the area we were looking for is also the area of a rectangle.\u00a0 The length is (x + y) and the width is (x – y).\u00a0 That gives us a new formula for this area:<\/p>\n Area = (x + y)(x \u2013 y)<\/i><\/strong><\/p>\n But we are talking about the same area both times.\u00a0 So what we have now is a geometric reason to believe that the difference of two squares can be factored:<\/p>\n \u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0\u00a0 x2<\/sup> \u2013 y2 <\/sup>= (x + y)(x \u2013 y)<\/i><\/strong><\/p>\n How important is this?\u00a0 Hmm.\u00a0 Within the context of high school math (and SAT math), it is apparently one of the most important factoring facts that there is.\u00a0 In physics class, I can only think of one setting where we used this. (We were deriving a rule about velocities before and after an elastic collision, in case you were wondering.)<\/p>\n The math we teach should either be useful or interesting.\u00a0 To me, the difference of two squares is more interesting when we\u00a0use pictures.\u00a0 And the idea of carving up the same area two different ways to see what you learn can be very powerful and lead to unquestionably important results.\u00a0 More about this in the next post.<\/p>\n","protected":false},"excerpt":{"rendered":" \u2026of two squares. Suppose we start with a square with side x and remove a smaller square with side y. The remaining area (shown in blue) is literally \u201cthe difference of two squares\u201d. We can find its area by subtracting … Continue reading <\/a><\/p>\n<\/a><\/p>\n