Loading the lesson
Loading the lesson
Search AllRounder.ai
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Search the courses, subjects, tracks, games and features, or jump straight to a page.
Learn it your way
A short class with Sarah and her students. The other ways are under More.
Sign up free to listen. Transcripts are free to read.
Today we will start with monomials. A monomial is a single term that contains a coefficient and one or more variables. Can anyone give me an example of a monomial?
How about 3x?
Exactly! 3x is a monomial. What do you think 0xy is? Is it a monomial?
No, because it has a coefficient of zero, so it equals zero!
Right! Now let's move to multiplying monomials.
When multiplying two monomials like 3x and 4y, what do we do with the coefficients?
We multiply them together!
Correct! So how would we decide what the new coefficient would be for 3x * 4y?
We would multiply 3 and 4, giving us 12.
Great job! Now if we multiply 3x by -2y, what's our result?
It would be -6xy!
Now let’s look at the variables. When multiplying, what’s the rule for combining the variables?
We add the exponents of like variables.
Correct! So if we multiply x^2 and x^3, what do we get?
x^{2+3} which is x^5.
Excellent! Remember the rule: a^m * a^n = a^{m+n}.
Let’s do some examples. What is 5x * 3x^2?
It’s 15x^{1+2} which equals 15x^3.
Fantastic! Now what about 5x * -4xy?
That’s -20x^{1+1}y, which simplifies to -20x^2y.
Exactly! Let’s remember these steps as we tackle more complex multiplication.
An algebraic expression with one term, such as 5x.
The numerical factor in a term of a polynomial, e.g., in 4xy the coefficient is 4.
When multiplying, multiply coefficients and add the exponents of like variables.
a(b + c) = ab + ac, useful when multiplying two monomials.
Multiply the numbers, combine the facts, add the powers, and see the impacts.
Once upon a time, there lived two numbers, 2 and 3, who wanted to join hands. When they met, they found they could create 6 together. They also summoned their friends x and y to multiply and dance in harmony producing new terms.
Remember: M.C.A! Multiply Coefficients, Add exponents.
M.M.E: Monomials Multiply Easily!
Term
What is a monomial?
Click to flip
Term
How do you multiply monomials?
Click to flip
Term
What happens when a negative is multiplied by a positive?
Click to flip
An algebraic expression consisting of a single term. Examples include 3x, -4y^2, 5xyz.
The numerical factor in a term of a polynomial or monomial. For example, in 4x, the coefficient is 4.
A number indicating how many times to multiply the base. For example, in x^2, the exponent is 2, meaning x is multiplied by itself once.
A symbol used to represent a quantity that can change, commonly represented by letters like x, y, etc.
This section introduces the multiplication of two monomials, showing how to multiply their coefficients and variables.
The section covers the process of multiplying two monomials, explaining the importance of multiplication rules for coefficients and variables. It demonstrates various examples to illustrate how to deal with negative signs and the properties of exponents.
In algebra, a monomial is a single term consisting of a coefficient and one or more variables raised to non-negative integer powers. When multiplying two monomials, we use the distributive property and the laws of exponents.
The general rule for multiplication of monomials involves multiplying the coefficients (numerical parts) together and then multiplying the variable parts, adding the exponents of any like variables.
Basic Examples:
3x by 4x^2 results in:3x * 4x^2 = (3 * 4) (x^1 * x^2) = 12x^{1+2} = 12x^3
Involving a Negative Coefficient:
-2y, multiplying by 5y gives:-2y * 5y = (-2 * 5)(y^1 * y^1) = -10y^{1+1} = -10y^2
The section also covers how to handle additional variables and constants within monomials. The multiplication operation applies equally regardless of the complexity, whether it's between positive, negative, or zero coefficients and any number of variables.
Overall, understanding how to multiply monomials is fundamental to more complex algebraic expression manipulations such as polynomials.