8.4.1 - Multiplying a monomial by a binomial

Interactive Audio Lesson

Listen to a student-teacher conversation explaining the topic in a relatable way.

Understanding Monomials and Binomials

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Today we're going to talk about monomials and binomials. Who can tell me what a monomial is?

Student 1
Student 1

Is it a math expression with only one term?

Teacher
Teacher

Exactly! And a binomial, can someone explain that?

Student 2
Student 2

A binomial has two terms, right?

Teacher
Teacher

Correct! For example, `5x + 2` is a binomial. Remember, when multiplying a monomial by a binomial, we use the distributive law to help us.

Student 3
Student 3

How does that work exactly?

Teacher
Teacher

Great question! Let's use `3x` and the binomial `5y + 2`. We distribute and multiply each term. It looks like this: `3x × (5y + 2) = (3x × 5y) + (3x × 2)`, which simplifies to `15xy + 6x`. Remember the acronym 'DISTRIBUTE' to aid your memory: 'Distribute Each Term'.

Student 4
Student 4

So we just multiply like we would with numbers?

Teacher
Teacher

Exactly! Let's summarize: we multiply each part of the binomial by the monomial. Who can give me another example?

Applying the Distributive Property

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Let's dive into applying the distributive property! Who can remind us what it means?

Student 1
Student 1

It means to multiply each term in the parentheses by what’s outside.

Teacher
Teacher

Exactly! For instance, with `-2a × (3b - 4)`, we get `-2a × 3b + (-2a) × (-4)`. What do we get?

Student 3
Student 3

That would be `-6ab + 8a`.

Teacher
Teacher

Well done! Notice how two negatives make a positive. Can anyone think of why we might reorder terms?

Student 2
Student 2

To simplify calculations! If we multiply `(3b - 4) × -2a`, we'd end with the same terms but possibly different signs!

Teacher
Teacher

Great observation! This property allows flexibility in computation.

Student 4
Student 4

Can we also multiply a binomial with another binomial using the same rules?

Teacher
Teacher

Yes! As we progress, we'll practice that, reinforcing our understanding of these laws.

Working with Negative Coefficients

Unlock Audio Lesson

Signup and Enroll to the course for listening the Audio Lesson

Teacher
Teacher

Next, let’s tackle expressions with negative numbers. For example, what happens with `-3x(5y + 2)`?

Student 1
Student 1

You would apply the same principle, right?

Teacher
Teacher

Absolutely! We would do `(-3x) × 5y + (-3x) × 2`, resulting in `-15xy - 6x`. Remember: 'Negative times Positive equals Negative; Negative times Negative equals Positive' – that’s a useful saying!

Student 2
Student 2

Could we rewrite it as `(-3x)(5y) + (-3x)(2)` to see it clearer?

Teacher
Teacher

Yes! It helps visualize the operation. Consistent practice ensures you understand these transformations.

Student 3
Student 3

Can you summarize again how to notice when signs change?

Teacher
Teacher

Sure! Just keep in mind the rules of signs when multiplying—this will guide you through.

Introduction & Overview

Read a summary of the section's main ideas. Choose from Basic, Medium, or Detailed.

Quick Overview

This section covers how to multiply a monomial by a binomial using the distributive law.

Standard

It provides a method for multiplying monomials and binomials, particularly through the distributive property, ensuring students grasp the structured approach of multiplying each term in the binomial by the monomial and combining like terms.

Detailed

Multiplying a Monomial by a Binomial

In this section, we explore the multiplication of a monomial by a binomial, emphasizing the use of the distributive law to facilitate the process. A monomial is defined as an expression containing only one term, while a binomial is an expression that contains two terms. The distributive property allows us to expand expressions effectively.

To multiply a monomial, such as 3x, by a binomial, like 5y + 2, we use the formula:

3x × (5y + 2) = (3x × 5y) + (3x × 2).

Following the multiplication, we combine the results: 15xy + 6x. The section further illustrates that the order of multiplication does not affect the outcome, as shown by the example that reverses the positions of the monomial and binomial. This foundational concept is critical for understanding more complex polynomial operations later in algebra.

Youtube Videos

Multiplying a Monomial by a Binomial - Algebraic Expressions & Identities | Class 8 Maths Chapter 9
Multiplying a Monomial by a Binomial - Algebraic Expressions & Identities | Class 8 Maths Chapter 9
How to Multiply a Monomial by a Binomial? || Algebraic Expression || C.B.S.E. Grade 8 Mathematics
How to Multiply a Monomial by a Binomial? || Algebraic Expression || C.B.S.E. Grade 8 Mathematics
Multiplying a Monomial by a Binomial | Class 8 Maths Chapter 9 | Algebraic Expression and Identities
Multiplying a Monomial by a Binomial | Class 8 Maths Chapter 9 | Algebraic Expression and Identities
Algebraic Expressions & Identities| Multiplication of Monomial by a Polynomial Part-1 #ncert #class8
Algebraic Expressions & Identities| Multiplication of Monomial by a Polynomial Part-1 #ncert #class8
How to Multiply a Monomial by a Monomial? || Algebraic Expressions || C.B.S.E. Grade 8 Mathematics
How to Multiply a Monomial by a Monomial? || Algebraic Expressions || C.B.S.E. Grade 8 Mathematics
Multiplying a Monomial by a Monomial NCERT Examples 3 & 4 | Class 8 Maths Chapter 8 | CBSE 2024-25
Multiplying a Monomial by a Monomial NCERT Examples 3 & 4 | Class 8 Maths Chapter 8 | CBSE 2024-25
Multiplication of monomial by binomial & trinomial | Algebraic expressions | Class 8 Maths Chapter 9
Multiplication of monomial by binomial & trinomial | Algebraic expressions | Class 8 Maths Chapter 9
Algebra: Identify monomial, binomial, trinomial and polynomial
Algebra: Identify monomial, binomial, trinomial and polynomial
🤔How to simplify algebraic expressions??? Algebraic Expressions/Short Tricks #shorts #shortsfeed
🤔How to simplify algebraic expressions??? Algebraic Expressions/Short Tricks #shorts #shortsfeed
Maths Algebraic Expressions part 12 (Multiply Monomial with Polynomial) CBSE Class 8
Maths Algebraic Expressions part 12 (Multiply Monomial with Polynomial) CBSE Class 8

Definitions & Key Concepts

Learn essential terms and foundational ideas that form the basis of the topic.

Key Concepts

  • Distributive Law: Necessary rule for multiplying monomials with polynomials.

  • Term Multiplication: Each term in the binomial or polynomial must be multiplied by the monomial.

Examples & Real-Life Applications

See how the concepts apply in real-world scenarios to understand their practical implications.

Examples

  • Example 1: Multiply 3x by the binomial 5y + 2 to get 15xy + 6x.

  • Example 2: Multiply -2a by 3b - 4 to receive -6ab + 8a.

Memory Aids

Use mnemonics, acronyms, or visual cues to help remember key information more easily.

🎵 Rhymes Time

  • To multiply a mono and a bino,/ Just distribute as you go,/ Don’t forget to combine the like,/ Or your answer may take a hike.

📖 Fascinating Stories

  • Once there was a clever little monomial named 3x who had a special friendship with the binomial 5y + 2. They loved to party, so every time they met, they multiplied their terms and had fun!

🧠 Other Memory Gems

  • Daisy Eats Sweet Bananas - for 'Distribute Each term in the Sum of the Binomial'.

🎯 Super Acronyms

MATH - Monomial and a Binomial Together Harmoniously.

Flash Cards

Review key concepts with flashcards.

Glossary of Terms

Review the Definitions for terms.

  • Term: Monomial

    Definition:

    An algebraic expression consisting of a single term, such as 3x.

  • Term: Binomial

    Definition:

    An algebraic expression containing two terms, such as 5y + 2.

  • Term: Distributive Law

    Definition:

    A property that states a(b + c) = ab + ac, used for distributing multiplication over addition.

  • Term: Coefficient

    Definition:

    A numerical factor in a term, such as 3 in 3x.