# Lesson 23

Polynomial Identities (Part 1)

### Lesson Narrative

This is the first of two lessons focusing on polynomial identities. The purpose of this lesson is for students to investigate expressions in order to understand that a polynomial identity is defined as an equation where the expression on the left has the same value for all possible inputs $$x$$ as the expression on the right.

In the warm-up and following activity, students explore the difference of the squares of two consecutive integers, calling back to the identity $$a^2 - b^2 = (a+b)(a-b)$$ they have worked with in earlier grades. Then students explore several cases of an identity where application of the distribution property leads to an expression with fewer terms than might be expected (MP8). This particular identity will be revisited in a future lesson where students derive the formula for the sum of a geometric series.

### Learning Goals

Teacher Facing

• Comprehend what a polynomial identity is.
• Prove some common identities.

### Student Facing

• Let’s learn about polynomial identities.

### Student Facing

• I understand what an identity is in mathematics.

Building Towards

### Glossary Entries

• identity

An equation which is true for all values of the variables in it.