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Master Equivalent Expressions of Polynomials | Math Guide

EQAO Grade 9 Math: Master Core Concepts & Skills

Ratios, Rates, and Proportions

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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

Square Roots

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Pythagorean Theorem

Introduction to pythagorean theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Rational Numbers

Comparing and ordering rational numbers

Comparing decimal numbers

Comparing fractions

Solving problems with rational numbers in decimal form

Mixed Operations with Decimals

Mixed Operations

Mixed Operations with Decimals Bracket

Mixed Operations with Bracket Square

Solving problems with rational numbers in fraction form

Operations with fractions

Determine square roots of rational numbers

Square roots of rational numbers

Powers and Exponents

Using exponents to describe numbers

Expanded powers

Exponent rules

Single Power Expressions

Dividing powers

Multiplying powers

Order of operations with exponents

Using exponents to solve problems

Proportional Relationships

Understanding graphs of proportional relationships

Linear relations

Using tables of values to graph proportional relationships

Linear relation

Applications of proportional relationships

Identifying proportional relationships

Linear Ralations

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

Reading linear relation graphs

Solving linear equations by graphing

Solving Linear Equations

Solving linear equations using multiplication and division

Two-step Linear Equations LHS

Two-step Linear Equations RHS

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving two-step linear equations: ax + b = c, x/a + b = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations using distributive property: a(x + b) = c

Solving linear equations with variables on both sides

Introduction to Relations and Functions

Relationship between two variables

Understand relations between x- and y-intercepts

Domain and range of a function

Identifying functions

Function notation

Linear Functions

Distance formula: \(d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Distance formula: <katex>d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}</katex>

Distance formula

Midpoint formula: \(M = ( \frac{x_1+x_2}2  ,\frac{y_1+y_2}2)\)

Midpoint formula

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Midpoint formula: <katex>M = ( \frac{x_1+x_2}2 ,\frac{y_1+y_2}2)</katex>

Slope equation: \(m = \frac{y_2-y_1}{x_2- x_1}\)

Slope equation: <katex>m = \frac{y_2-y_1}{x_2- x_1}</katex>

Slope intercept form: y = mx + b

General form: Ax + By + C = 0

Point-slope form: \(y - y_1 = m (x - x_1)\)

Graphing linear functions using table of values

Graphing linear functions using x- and y-intercepts

Graphing from slope-intercept form y=mx+b

Graphing linear functions using a single point and slope

Word problems of graphing linear functions

Rate of change

Parallel and perpendicular lines in linear functions

Applications of linear relations

Introduction to Polynomials

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

Adding and subtracting polynomials

Multiplication and Division of 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

Introduction to 3-Dimensional Objects

Introduction to surface area of 3-dimensional shapes

Nets of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Surface Area and Volume

Surface area and volume of prisms

Surface area and volume of pyramids

Surface area and volume of cylinders

Surface area and volume of cones

Surface area and volume of spheres

Circle Geometry

Angles in a circle

Chord properties 

Tangent properties

Data Management

Influencing factors in data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Scatter plots and correlation

Census and bias

Census and Bias

Classifying Bias

Linear Programming

What is linear programming?

Finding Optimal Values Given Constraints In Slope-Intercept Form

Finding Optimal Values Given Constraints In Standard Form

Linear programming word problems

EQAO Grade 9 Principles of Math

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Intro

- Hi, welcome to this question right here. So we're trying to write an equivalent expression. Equivalent expression means something that is exactly the same. They don't look the same, but they are the same. Okay, but you need to have seven terms, so there's multiple of different ways of doing this, actually infinity number of ways in doing this question. So I'm just going to do one example, it's your choice to come up with different answers, okay? The idea is the same. You need to get x square plus 2x plus three as your final answer, okay? 
I can quickly show you how the first way I'm going to do this is-- Let's say how many ways we're going to x square. Maybe I have two x square minus an x square. That will also give me one x square, right? 
Simple enough. What about the 2x? Well, I can say plus, let's change to another color. Plus four x and then minus 2x because these two guys right here will give me two x in total so that is my final answer. So far I got one, two, three, four, four terms now. So I need three more terms to satisfy the question, right? The question says seven terms in total. I need a three at the very end. So any ideas to get a three. Again, the number of the answers you're going to get for this question is like, I don't know how many. Okay, tons and tons. So how do you get a three at the very end? Well, let's try this way. How about let's plus a 10. So 10, let's say you subtract a two. I ran out of space. Minus two is eight. How do you get a three? Well, eight minus five. So try another five. Okay? 
So clearly if you just look at the colors, we&apos;ve got two yellows, two greens and three purples. So all together it's seven terms in total, and if you simplify these guys over here. I can show you really quickly again but you probably know the answer anyway. Two x square minus x square is x square. See, they're the same so far. Take the green one again, so the green one, we have 4x minus 2x. So it's plus 2x. What about the last type of the variables, not variables. The constants here, 10 minus two, minus five? The answer is three, and that's what happens. We&apos;ve got x square plus 2x and the minus three. These guys here, and these guys here are equivalent, the same, but they are-- Well, originally they look different but once you put it all together, they are the same. Okay? This is just to check and your final answer is not this. Your final answer is here, all these guys. Okay? One, two, three, four, five, six, seven, seven terms in total. All right, thanks for watching.

A polynomial may contain multiple terms. The variable terms have a coefficient and a <a href="[[glossary.html|{"keyword":"Variable"}]]">variable</a>. Terms with the same variables are called like terms, and they can be combined together. It allows us to write equivalent expressions of polynomials with more or less terms.

Equivalent algebraic expressions

What are equivalent expressions of polynomials?

Understanding integer division

Applications of integer operations