Task 1: Applying the Binomial Theorem Question 1
Use the binomial theorem to expand a binomial expression.
Question 2
a. Determine the eighth term of the binomial expression.
b. Determine the positions of three terms of the expanded form of the binomial expression.
Task 2: Expanding a Binomial Expression with Pascal's Triangle
a. Identify a and b in the binomial expression.
b. Identify the row of Pascal's triangle that shows coefficients in the expansion of the binomial expression.
C. Find the terms of the binomial expansion.
Task 3: Relating a Polynomial Identity to Pythagorean Triples
a. Prove a polynomial identity.
b. Write the identity as an equation.
C. Generate Pythagorean triples given values of x and side lengths.
d. Write observations about the patterns in the Pythagorean triples.
e. Generate a two-variable identity.
f. Generate a Pythagorean triple for given values of x, y, and side lengths.