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Algebra 1: Arithmetic with Polynomials and Rational Expressions – A-APR ELG.MA.HS.A.3 Perform arithmetic operations on polynomials. A-APR.A.1 Understand that polynomials form a system analogous to the integers, namely, they are closed under the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials. Arithmetic with Polynomials and Rational Expressions – A-APR ELG.MA.HS.A.5: Use polynomial identities to solve problems. A-APR.C.5 (+) Know and apply the Binomial Theorem for the expansion of (x + y)n in powers of x and y for a positive integer n, where x and y are any numbers, with coefficients determined for example by Pascal’s Triangle.1 Algebra 2: Arithmetic with Polynomials and Rational Expressions – A-APR ELG.MA.HS.A.5: Use polynomial identities to solve problems. A-APR.C.4 Prove polynomial identities and use them to describe numerical relationships. For example, the polynomial identity (x2 + y2)2 = (x2 – y2)2 + (2xy)2 can be used to generate Pythagorean triples. Students will demonstrate command of the ELG by: Applying the Binomial Theorem for the expansion of (x + y)n and other binomials. Using Pascal’s Triangle to determine the coefficients in binomial expansions. Vocabulary: • Binomial Theorem • Coefficient • Expansion • Pascal’s Triangle Sample Assessment Questions: 1 The Binomial Theorem can be proved by mathematical induction or by a combinatorial argument 1) Standard(s): A-APR.C.5 Item Prompt: Correct Answer(s) Source: www.illustrativemathematics.org/content-standards/HSA/APR/C/5/tasks/1654 2) Standard (s): A-APR.C.5 Source: www.khanacademy.org/math/algebra2/polynomial-functions/binomial-theorem/e/binomial-theorem Item Prompt Expand the expression (5x – y)3 using the Binomial Theorem. Correct Answer(s) 125x3 – 75x2y + 15xy2 – y3