Exponents and Polynomials - XYZ Custom Plus

RESEARCH PROJECTBinomial ExpansionsThe title on the following diagram is BinomialExpansions because each line gives the expansionof the binomial x + y raised to a wholenumberpower.Binomial Expansions(x + y) 0 = 1(x + y) 1 = x + y(x + y) 2 = x 2 + 2xy + y 2(x + y) 3 = x 3 + 3x 2 y + 3xy 2 + y 3(x + y) 4 =(x + y) 5 =The fourth row in the diagram was completedby expanding (x + y) 3 using the methods developedin this chapter. Next, complete the diagramby expanding the binomials (x + y) 4 and(x + y) 5 using the multiplication procedures youhave learned in this chapter. Finally, study thecompleted diagram until you see patterns thatwill allow you to continue the diagram onemore row without using multiplication. (Onepattern that you will see is Pascal’s triangle,which we mentioned in the preceding groupproject.) When you are finished, write an essayin which you describe what you have done andthe results you have obtained.612Chapter 9 Exponents and Polynomials