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How to multiply polynomials with monomials

Grade 9 Math: Master Core Concepts & Problem Solving

B1.1 research a number concept to tell a story about its development and use in a specific culture, and describe its relevance in a current context

Understanding the number systems

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B1.2 describe how various subsets of a number system are defined, and describe similarities and differences between these subsets

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Rational vs. Irrational numbers

Place value

Comparing and ordering numbers

Comparing Integers

Comparing Numbers

Comparing Fractions

B1.3 use patterns and number relationships to explain density, infinity, and limit as they relate to number sets

Using exponents to describe numbers

Expanded powers

Patterns

Patterns — Word Problem

B2.1 analyse, through the use of patterning, the relationship between the sign and size of an exponent and the value of a power, and use this relationship to express numbers in scientific notation and evaluate powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Product rule of exponents

Scientific notation

B2.2 analyse, through the use of patterning, the relationships between the exponents of powers and the operations with powers, and use these relationships to simplify numeric and algebraic expressions

Order of operations with exponents

Using exponents to solve problems

Quotient rule of exponents

Power of a product rule

Power of a quotient rule

Power of a power rule

Simplify the power

Negative exponent rule

Combining the exponent rules

B3.1 apply an understanding of integers to describe location, direction, amount, and changes in any of these, in various contexts

Applications of integer operations

Multiple Integer Operations

Three Step Integer Operations Combined Multiply Divid

Three Step Integer Operations Divide Add Or Minus Multiply

Three Step Integer Operations Divide Add Or Minus

Three Step Integer Operations Multiply Add Minus Divide

Three Step Integer Operations Multiply Add Or Minus

Subtracting integers

Subtracting 1-digit integers

Subtracting 2-digit integers

B3.2 apply an understanding of unit fractions and their relationship to other fractional amounts, in various contexts, including the use of measuring tools

Solving problems with rational numbers in fraction form

Operations with fractions

Applications of fraction operations

Fraction Operations

Converting repeating decimals to fractions

B3.3 apply an understanding of integers to explain the effects that positive and negative signs have on the values of ratios, rates, fractions, and decimals, in various contexts

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Ratios

Ratios - Find The Missing Value LHS

Ratios - Find The Missing Value RHS

Equivalent Ratios

Rates

Find the Biggest Rate 

Find the Unit Price 

Unit Rate Fill in Box

Find the Quickest Rate 

Unit Rate

Proportions

Proportions — Missing Denominator

Proportions — Missing Numerator

Proportions - Find the Missing Denominator LHS

Proportions - Find the Missing Denominator RHS

Proportions - Find the Missing Numerator LHS

Proportions - Find the Missing Numerator RHS

B3.4 solve problems involving operations with positive and negative fractions and mixed numbers, including problems involving formulas, measurements, and linear relations, using technology when appropriate

Fractions: Multiplying proper fractions

Multiply Proper Fractions — 1 Digit Fractions

Multiplying improper fractions and mixed numbers

Multiply Mixed Numbers

Dividing fractions and mixed numbers

Divide Fractions and Mixed Numbers – Word Problem

Dividing Mixed numbers

Dividing Mixed Numbers

Adding and subtracting decimals

Subtracting Decimals — Data Table

Ordering Decimals — Data Table

Decimals – Word Problem

Adding Decimals

Subtracting Decimals

Multiplying decimals

Multiplying Decimals

Dividing decimals

Dividing Decimals

Order of operations (PEMDAS)

Identify the Order of Operations

Order of Operations — Word Problem

B3.5 solve problems involving ratios, rates, and percent in various contexts, including contexts connected to real-life applications of data, measurement, geometry, linear relations, and financial literacy

Taxes, discounts, tips and more

Discounts — Word Problem

Taxes — Word Problem

Percentage - Applying a Discount Price– Word Problem

Percentage - Applying a Discount Percent – Word Problem

Percentage - Applying a Tax Total – Word Problem

Percentage - Applying a tax Percent – Word Problem

Simple interest

Simple Interest — Word Problem

Basic Concepts of Simple Interest – Word Problem

Borrowing Money for More Than One Year  – Word Problem

Investigate the Advantages of Borrowing Money  – Word Problem

Representing percents

Representing Percents

Representing Percents — Word Problem

Representing Percents Two Graphs – Word Problem

Percents, fractions, and decimals

Conversion — Decimal to Fraction

Conversion — Decimal to Percent

Conversion — Fraction to Decimal

Conversion — Fraction to Percent

Conversion — Percent to Decimal

Conversion — Percent to Fraction

Percents – Word Problem

Convert a Decimal to a Fraction

Convert a Decimal to a Percent

Convert a Fraction to a Decimal

Convert a Fraction to a Percent

Convert a Percent  to a Decimal

Convert a Percent to a Fraction

Percents Fractions And Decimals – Word Problem

Percent of a number

Percent of a Number

percent of a number – Word Problem

Percent of a Number  Fraction Percent

Percent of a Number Integer Percent 

Percent of a number number With Decimal Percent 

Percent of a Number  Three Digits Number Percent

Adding and multiplying percents

Add and Multiply Percents — Word Problem

Add and Multiply Percents – Word Problem

C1.1 research an algebraic concept to tell a story about its development and use in a specific culture, and describe its relevance in a current context

What is a polynomial?

Classifying Polynomials

C1.2 create algebraic expressions to generalize relationships expressed in words, numbers, and visual representations, in various contexts

Characteristics of polynomials

What are polynomials

Representing patterns in linear relations

Represent Patterns in Linear Relations Equation Decimal

Represent Patterns in Linear Relations Equation Integer Start From 0

Represent Patterns in Linear Relations Equation Integer Start From 1

Represent Patterns in Linear Relations Equation Negative Decimal

Identify the Linear Equation

Evaluating algebraic expressions

Evaluating Algebraic Expressions

C1.3 compare algebraic expressions using concrete, numerical, graphical, and algebraic methods to identify those that are equivalent, and justify their choices

Equivalent expressions of polynomials

Polynomial components

C1.4 simplify algebraic expressions by applying properties of operations of numbers, using various representations and tools, in different contexts

Adding and subtracting polynomials

Multiplying and dividing monomials

Divide a monomial by a monomial

Multiply a monomial by a monomial

Multiplying polynomials by monomials

Multiply a polynomial by a monomial

Dividing polynomials by monomials

Multiplying monomial by monomial

We&apos;ve got you covered with our complete help for Grade 9 math, whether it&apos;s for <a href="http://www.eqao.com/en/assessments/grade-9-math">EQAO</a> (Ontario), grade 9 math <a href="https://education.alberta.ca/provincial-achievement-tests/about-the-pats/">PAT</a> (Alberta), grade 9 math <a href="http://www.ed.gov.nl.ca/edu/k12/evaluation/crts/intermediate/">Provincial Assessment</a> (Newfoundland) or <a href="http://www.gov.pe.ca/eecd/index.php3?number=1027081&lang=E">IMA</a> (PEI).

Aligned with your class or textbook, you will get grade 9 math help on topics like Circle geometry, Linear equations, Dividing polynomials, Exponents, Surface area, Rational numbers, and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 9 math questions. Then, strengthen your understanding with tons of grade 9 math practice. 

All our lessons are taught by experienced Grade 9 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Grade 9 Math (MTH1W)

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Overview

Multiplying polynomials by monomials

What You'll Learn

Multiply monomials by polynomials using the distributive property

Apply the area model to visualize polynomial multiplication

Combine terms correctly when multiplying expressions with multiple variables

Recognize that each term in the polynomial must be multiplied by the monomial

Simplify polynomial products involving decimals, fractions, and negative terms

What You'll Practice

Multiplying single-term expressions by binomials and trinomials

Using area models to set up and solve multiplication problems

Working with decimal coefficients and mixed variable terms

Solving word problems involving rectangular areas and dimensions

Why This Matters

Before You Start — Make Sure You Can:

This Unit Includes

10 Video lessons

Practice exercises

Skills

Polynomials

Monomials

Distributive Property

Area Model

Algebraic Multiplication

Simplifying Expressions

Variables