# Exponents and Exponential Functions

## Objective

Multiply polynomials using properties of exponents and properties of operations.

## Common Core Standards

### Core Standards

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• 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.

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• 7.EE.A.1

• 8.EE.A.1

• 8.EE.C.7

## Criteria for Success

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1. Apply the distributive property to multiply a monomial by a polynomial.
2. Apply the distributive property more than once to multiply a polynomial by a polynomial.
3. Use precision when simplifying polynomial expressions; multiply coefficients of terms and add the exponents of like bases (Standard for Mathematical Practice 6).

## Anchor Problems

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### Problem 1

Find the product.

${4y^2(-3y+6y^5-4)}$

### Problem 2

Find the product.

${(y+1)(y^3-2y+5)}$

### Problem 3

${2x^3(3x^4-x^2+x)-(2x^5-x^7)}$

## Problem Set

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The following resources include problems and activities aligned to the objective of the lesson that can be used to create your own problem set.

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### Problem 1

Must the product of three polynomials again be a polynomial?

#### References

EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 9Exit Ticket, Question #1

Algebra I > Module 1 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..

### Problem 2

Find ${(w^2+1)(w^3-w+1)}$.

#### References

EngageNY Mathematics Algebra I > Module 1 > Topic B > Lesson 9Exit Ticket, Question #2

Algebra I > Module 1 > Topic B > Lesson 9 of the New York State Common Core Mathematics Curriculum from EngageNY and Great Minds. © 2015 Great Minds. Licensed by EngageNY of the New York State Education Department under the CC BY-NC-SA 3.0 US license. Accessed Dec. 2, 2016, 5:15 p.m..