About Us

Why Choose StudyPug

How it works

Pricing

Testimonials

Contact Us

Blog

Basic Math

Algebra

Geometry

Trigonometry

Calculus

Linear Algebra

Differential Equations

Statistics

Chemistry

Organic Chemistry

Physics

Microeconomics

For Students

For Parents

For Home Schoolers

For Teachers

Australia

Canada

Ireland

New Zealand

Singapore

United Kingdom

United States

Sitemap

Terms of Service

Privacy Policy

Master Equivalent Expressions of Polynomials | Math Guide

Grade 9 Math: Master Core Concepts & Problem Solving

Develop number sense

auto-gen

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

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

Squares and square roots

Square Root of a Perfect Square

Estimating square roots

Use patterns to describe the world and solve problems

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

Understanding graphs of linear relationships

Linear relations

Understanding tables of values of linear relationships

Linear relation

Applications of linear relationships

Represent algebraic expressions in multiple ways

Compound inequalities

Analyze the Alternate Form of Compound Inequalities: AND

Compound linear inequalities

Evaluate Compound Inequalities: And

Characteristics of polynomials

What are polynomials

Equivalent expressions of polynomials

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

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

Solving linear equations with variables on both sides

Express linear inequalities graphically and algebraically

Graph the Inequality

Linear Inequalities – Word Problem 

Linear inequalities

Solving one-step linear inequalities

One-step Linear Inequalities

One-step linear inequalities

One-step Linear Inequalities Decimal

One-step Linear Inequalities Decimal with Fraction

One-step Linear Inequalities Fraction

Solve One Step Linear Inequalities Find Solution– Word Problem

One-step Linear Inequalities — Word Problem

Solving multi-step linear inequalities

Multi-step Linear Inequalities

Two-step Linear Inequalities

Multi-step linear inequalities

Two-step linear inequalities

Solve Multi-step Linear Inequalities – Word Problem 

Solve Multi Step Linear Inequalities Solve Equation – Word Problem

Solve Multi Step Linear Inequalities Equation – Word Problem

Model and solve one-step linear equations: ax = b, x/a = b

One-step Linear Equations

One Step Linear Equations — Word Problem

One-step equations

One-step Equations LHS

One-step Equations RHS

Model And Solve One Step Linear Equations Divide – Word Problem

Model And Solve One Step Linear Equations Multiply – Word Problem

Solving two-step linear equations using addition and subtraction: ax + b = c

Two-step Linear Equations

Solve Linear Equations Using Addition and Subtraction – Word Problem

Two-step Linear Equations — Word Problem

Solving two-step linear equations using multiplication and division: x/a + b = c

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

Solve Linear Equations Using Distributive Property – Word Problem

Solving literal equations

Use direct and indirect measurement to solve problems

Angles in a circle

Chord properties

Tangent properties

Pythagorean theorem

Pythagorean Theorem

Using the pythagorean relationship

Applications of pythagorean theorem

Describe the characteristics of 3-D objects and 2-D shapes, and analyze the relationships among them

Surface area of 3-dimensional shapes

Enlargements and reductions with scale factors

Scale diagrams

Similar triangles

Similar polygons

Introduction to surface area of 3-dimensional shapes

Surface area of prisms

Surface Area of Prisms Rectangle

Calculate the Surface Area

Surface area of cylinders

Describe and analyze position and motion of objects and shapes

Line symmetry

Rotational symmetry and transformations

Collect, display and analyze data to solve problems

Influencing factors in data collection

Data collection

Classification of data

Characteristics of Quantitative Data

Classify the Level of Measurement

Identify the Level of Measurement

Sampling methods

Sampling Methods

Use experimental or theoretical probabilities to represent and solve problems involving uncertainty

Probability

Determining probabilities using tree diagrams and tables

Probability of independent events

Probability with Venn diagrams

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

https://dmn92m25mtw4z.cloudfront.net/img/textbook/textbook-grade9math.png

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