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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