Multiply Binomials Like a Pro: Mastering Polynomial Multiplication

Algebra 2 Grades High School 4:44 Video
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Lesson Description

Learn how to multiply three binomials together using the distributive property. This lesson includes step-by-step examples and practice problems to help you master polynomial multiplication.

Video Resource

How to Multiply 3 Binomials

Mario's Math Tutoring

Duration: 4:44
Watch on YouTube

Key Concepts

  • Distributive Property
  • Combining Like Terms
  • Polynomial Multiplication
  • Binomial
  • Trinomial

Learning Objectives

  • Students will be able to multiply two binomials using the distributive property (or FOIL method).
  • Students will be able to multiply the result of two binomials by a third binomial.
  • Students will be able to simplify the resulting polynomial by combining like terms.
  • Students will be able to write the final answer in descending order of exponents.

Educator Instructions

  • Introduction (5 mins)
    Begin by reviewing the definition of a binomial and the distributive property. Briefly explain the process of multiplying two binomials. Show an example such as (x+1)(x+2).
  • Video Instruction (10 mins)
    Watch the 'How to Multiply 3 Binomials' video by Mario's Math Tutoring. Encourage students to take notes on the steps involved and the examples provided.
  • Example Walkthrough (10 mins)
    Work through the examples from the video on the board, explaining each step in detail. Emphasize the importance of careful distribution and combining like terms correctly. Use visuals to illustrate the process.
  • Guided Practice (15 mins)
    Provide students with practice problems involving multiplying three binomials. Start with simpler problems and gradually increase the complexity. Circulate the classroom to provide assistance and answer questions.
  • Independent Practice (10 mins)
    Assign independent practice problems for students to complete on their own. This will allow them to solidify their understanding of the concept. Collect the completed work for assessment.

Interactive Exercises

  • Pair-Share Problem Solving
    Divide students into pairs and give each pair a different set of three binomials to multiply. Have them work together to solve the problem and then share their solutions with the class.
  • Whiteboard Challenge
    Present a challenging problem on the whiteboard and have students work individually to solve it. After a set amount of time, have students compare their solutions and discuss any differences.

Discussion Questions

  • What is the distributive property and how does it apply to multiplying binomials?
  • Why is it important to combine like terms after multiplying?
  • Does the order in which you multiply the binomials matter? Why or why not?
  • Can you think of a real-world scenario where multiplying binomials might be useful?

Skills Developed

  • Applying the distributive property
  • Combining like terms
  • Polynomial manipulation
  • Problem-solving

Multiple Choice Questions

Question 1:

What is the first step in multiplying three binomials?

Correct Answer: Multiply the first two binomials together

Question 2:

Which property is used to multiply binomials?

Correct Answer: Distributive Property

Question 3:

What is a binomial?

Correct Answer: An expression with two terms

Question 4:

When multiplying x * x², what is the resulting exponent?

Correct Answer: 3

Question 5:

What does it mean to combine like terms?

Correct Answer: Adding terms with the same variables and exponents

Question 6:

After multiplying and simplifying, how should the final polynomial be written?

Correct Answer: In descending order of exponents

Question 7:

What is the result of (x + 2)(x - 2)?

Correct Answer: x² - 4

Question 8:

What is the coefficient of the x² term in the expansion of (x+1)(x+2)(x+3)?

Correct Answer: 6

Question 9:

If you multiply (x + a)(x + b)(x + c), what will be the constant term?

Correct Answer: abc

Question 10:

Which expression is equivalent to (x + 1)(x + 1)(x + 1)?

Correct Answer: x³ + 3x² + 3x + 1

Fill in the Blank Questions

Question 1:

A __________ is an algebraic expression containing two terms.

Correct Answer: binomial

Question 2:

The __________ property is used to multiply each term inside the parentheses by a term outside the parentheses.

Correct Answer: distributive

Question 3:

Terms with the same variable and exponent can be __________ together.

Correct Answer: combined

Question 4:

When multiplying variables, you __________ the exponents.

Correct Answer: add

Question 5:

After multiplying and combining like terms, the polynomial should be written in __________ order of exponents.

Correct Answer: descending

Question 6:

(x+1)(x+1) = x² + 2x + ______.

Correct Answer: 1

Question 7:

The expression (2x - 1)(x + 3) expands to 2x² + 5x - ______.

Correct Answer: 3

Question 8:

The result of (x)(x)(x) is x to the power of _________.

Correct Answer: 3

Question 9:

When multiplying (x - 2)(x + 2), the middle term cancels out because it equals _________.

Correct Answer: zero

Question 10:

The constant term in the expansion of (x + 1)(x + 2)(x + 3) is _________.

Correct Answer: 6

Educational Standards

A2.A.2.2:Add, subtract, multiply, divide, and simplify polynomial expressions. A2.A.2.1:Factor polynomial expressions including, but not limited to, trinomials, differences of squares, sum and difference of cubes, and factoring by grouping, using a variety of tools and strategies.

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