(r - s)^2 = (r - s) (r - s) = (r + (-s)) (r + (-s)) Use FOIL, First Outside Inside Last. This means multiply the first terms together, multiply the two terms at the center together (inside terms), multiply the terms on the outside together, and then multiply the last terms together. Then add these products up. First terms (in caps): (R + (-s)) (R + (-s)) Outside terms: (R + (-s)) (r + (-S)) Inside terms: (r + (-S)) (R + (-s)) Last terms: (r + (-S)) (r + (-S)) So (r - s)^2 = (r + (-s)) (r + (-s)) = product of first terms + product of outside terms + product of inside terms + product of last terms = (r x r) + (r x (-s)) + ((-s) x r) + ((-s) x (-s)) = r^2 + (-rs) + (-rs) + (-s)^2 = r^2 - rs - rs + s^2 = r^2 - 2rs + s^2 = r^2 + s^2 - 2rs