Mastering Technical Mathematics, Third Edition, 3rd Edition

11	Some Useful Shortcuts

Have you noticed that when two factors have the same terms but with the sign between them different, the product is the difference between the terms, each squared? For example, you can multiply the two terms (a + b)(a−b) to yield a²−b². You can also factorize a²−b² into (a+b)(a − b). This is a shortcut that you can use in working out some algebra problems. Let’s look at a few more.

SUM AND DIFFERENCE IN GEOMETRY

The sum and difference principle can be seen in geometry as well as in algebra. If you take the smaller square from the bigger square in Fig. 11-1, you are left with the shaded area. This is like taking b² from a². If you cut the upright piece off and lay it end-on to the other piece, the resulting rectangle ...