MAT 214 Prof. Erstenyuk Name: 1.2 Patterns and Pascal's Triangle Part III: Binomial Multiplication Patterns in Pascal's Triangle a.) What is (x+1)? (Hint: anything to the 0 power is _ b.) What is (x+1)?? c.) What is (x+1)2? Caution: it is not x2+12, but is gotten by multiplying (x + 1)(x + 1). d.) Where can the coefficients and constants of each answer be found in Pascal's triangle? The coefficient is the number in front of x, and the constant is the added on number. For x + 1, the coefficient in front of the x is a 1, so we have 1x + 1. Where do you see 1 1 in the triangle? Where do you see the coefficients and constants for your answer to part c? e.) What is (x+1)3? Hint: multiply the result of (x+1)2 by (x+1), then combine like terms and simplify. Check your answer using Pascal's triangle. Show how you know you are correct. f.) Make a conjecture as to what (x+1)* will equal, using Pascal's triangle. You do not have to multiply it all out to check! g.) Make a conjecture as to what (a+b) will equal, using Pascal's triangle