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How to multiply a polynomial with a polynomial

Grade 12 Math: Master Advanced Concepts & Skills

Geometric explorations

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Solving expressions using 45-45-90 special right triangles

Solving expressions using 30-60-90 special right triangles

Conics - Parabola

Conics - Circle

Conics - Ellipse

Conics - Hyperbola

Graphical representations of polynomial, logarithmic, exponential, and sinusoidal functions

Graphing exponential functions

Graphing transformations of exponential functions

Graphing logarithmic functions

Sine graph: y = sin x

Cosine graph: y = cos x

Tangent graph: y = tan x

Regression analysis

Equation of the best fit line

Combinatorics

One to one functions

Combining transformations of functions

Fundamental counting principle

Fundamental Counting Principle Involving Restrictions

Factorial notation

Path counting problems

Permutations

Combinations

Problems involving both permutations and combinations

Pascal's triangle

Pascal's Triangle

Pascal"s Triangle

Pascal"s triangle

Function notation (advanced)

Composite functions

Adding functions

Subtracting functions

Multiplying functions

Dividing functions

Operations of Functions – In a Nutshell

Inverse functions

Transformations of functions: Horizontal translations

Transformations of functions: Vertical translations

Reflection across the y-axis: y = f(-x)

Reflection across the x-axis: y = -f(x)

Transformations of functions: Horizontal stretches

Transformations of functions: Vertical stretches

Operations with functions

Inequalities of combined functions

Inequalities of Combined Functions

Even and odd functions

Difference quotient: applications of functions

Odds, probability, and expected value

Applications of linear relations

What is a polynomial?

Classifying Polynomials

Introduction to probability

Identify the Probability — Word Problem

Compound Probability

Reading Probability Models

Probability

Organizing outcomes

Calculating Outcomes

Probability of independent events

Comparing experimental and theoretical probability

comparing experimental and theoretical probability

Polynomial components

Multiplying monomial by monomial

Multiply a Monomial by a Monomial

Multiplying monomial by binomial

Multiplying binomial by binomial

Multiplying polynomial by polynomial

Reading and drawing Venn diagrams

Probability with Venn diagrams

Financial planning

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

Binomial theorem

Finance: Compound interest

Finance: Compound Interest

Finance: Future value and present value

Permutation vs. Combination

We&apos;ve got you covered with our complete help for Grade 12 math, whether it&apos;s Ontario curriculum, <a href="https://www.alberta.ca/writing-diploma-exams.aspx">Diploma exam</a> (Alberta), <a href="http://www.edu.gov.mb.ca/k12/assess/tests/index.html">Provincial test</a> (Manitoba) or <a href="https://www.saskatchewan.ca/residents/education-and-learning/departmental-exams">Departmental exam</a> (Saskatchewan).

Aligned with your class or textbook, you will get grade 12 math help on topics like Trigonometric identities, Vectors, Permutations and Combinations, Matrices, Polynomial functions and so many more. Learn the concepts with our video tutorials that show you step-by-step solutions to even the hardest grade 12 math questions. Then, strengthen your understanding with tons of grade 12 math practice. 

All our lessons are taught by experienced Grade 12 math teachers. Let&apos;s finish your homework in no time, and ACE that final.

Foundations of Mathematics 12

math

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Ex. 1:

- Hi, welcome to this question here. Well, we've got a binomial multiplying a trinomial. This is going to be a lot of a calculation because this 2a right here has to be multiplied by this, then this, and then this one here. And the same thing with the b, multiplied by the 2a, multiplied by the 5ab, and finally the 4. Oops, finally the 4 b square. Oh, what the cursor went out there for? 
So, it got like six, seven terms at the end, and we may have to do a little simplification later on. Here we go, 2a times 2a square, we've got ourselves the 4a to the power of 3, OK? 
Then we have the 2a times the negative 5ab, we've got a negative 10 a square times the b. And then the last one right here, we've got the 8 a and b square. Fair enough. The next one we go b times 2 square, we've got a 2 a square b, I like the a go before in front of the b. And then, the next one we have the negative 5 ab square. And the last one we have the 4 and that's gonna be a b cube. And you just gonna have to double check, so if you look across right here, do you see anything that they have in common? I've got an a square b right here and an a square b right there, so these two guys, let's just put brackets around them, actually a square. They have to be collected as alike terms. We've got an ab square here and an ab square, so these two guys right here have to be collected as alike terms. So, my final answer should turn out to be a 4a cube.And then I have to put these two guys together so, negative 10 and a positive 2, just gives you the negative 8 a square b. Then 8 and the negative 5 is going to get you the 3 ab square. And last, we've got a 4b cube at the very end. And that is your final answer. Thanks for watching.

When multiplying polynomials, we need to distribute each term in the first polynomial to every term in the second polynomial. Then, we combine any like terms.

Combining the exponent rules