[LESS INFO] 3 VIEWS | ADDED 03:31:55 05/09/08
Sections: 10.5, 11.4Topics: Systems of Nonlinear Equations, Binomial TheoremSection 10.5 is a perfect example of the interplay between algebra and geometry. How criminally, utterly ridiculous, then, that they don't actually have you do the geometry part in the homework - only the algebra. The topic is systems of nonlinear equations: nonlinear means parabolas, circles, or even ellipses and hyperbolas (which we didn't study.) Just as in chapter 3, we can solve a system of such equations using the methods of substitution or addition. And as in chapter 3, we can also graph the equations and the solutions will correspond to points of intersection. (And now that we're not just dealing with lines, sometimes there's more than one point of intersection!) Section 11.4 is totally different. It's a shortcut for finding powers of binomials. You, too, can figure out (x+1)^7 quickly without going through a long laborious multiplication! (And no, the answer isn't x^7 + 1 - that's that tempting siren again....) The key is to use something called Pascal's Triangle....
