Algebra Flashcards: F.O.I.L and Special Cases
16 Questions
100 Views

Choose a study mode

Play Quiz
Study Flashcards
Spaced Repetition
Chat to lesson

Podcast

Play an AI-generated podcast conversation about this lesson

Questions and Answers

What is a binomial?

a two-term polynomial

What is the product of (ab + 3)(ab - 3)?

a^2b^2 - 9

What is the correct product of (j + 7)(k - 5)?

jk - 5j + 7k - 35

What is the product of (n + 7)^2?

<p>n^2 + 14n + 49</p> Signup and view all the answers

What is the product of [(x + 1)(x - 1)]^2?

<p>x^4 - 2x^2 + 1</p> Signup and view all the answers

What is the product of (ab + 3)^2?

<p>a^2b^2 + 6ab + 9</p> Signup and view all the answers

What is the product of (r + s)^2?

<p>r^2 + 2rs + s^2</p> Signup and view all the answers

What is the correct product of (a + 8)(b + 3)?

<p>ab + 3a + 8b + 24</p> Signup and view all the answers

What is the product of (r - s)^2?

<p>r^2 - 2rs + s^2</p> Signup and view all the answers

What is the product of (2m - 9)^2?

<p>4m^2 - 36m + 81</p> Signup and view all the answers

What is the product of (2j + 7)(2j - 7)?

<p>4j^2 - 49</p> Signup and view all the answers

What is the correct product of (2x + 9)(x + 1)?

<p>2x^2 + 11x + 9</p> Signup and view all the answers

What is the product of (z - 12)(z + 12)?

<p>z^2 - 144</p> Signup and view all the answers

What does FOIL stand for?

<p>First, Outside, Inside, Last</p> Signup and view all the answers

How is a binomial squared calculated?

<p>Square the first term, double the product of the two terms, and then square the last term.</p> Signup and view all the answers

What results when binomials differ only by the sign between the terms?

<p>The difference of the square of the first term and the square of the last term.</p> Signup and view all the answers

Study Notes

Binomials

  • A binomial is defined as a polynomial with two terms.

Products of Binomials

  • The mental product of (ab + 3)(ab - 3) results in:

    • a²b² - 9, showcasing the difference of squares.
  • The product of (j + 7)(k - 5) simplifies to:

    • jk - 5j + 7k - 35, demonstrating distribution.

Squaring Binomials

  • Squaring (n + 7) provides:

    • n² + 14n + 49, derived from the formula (a + b)² = a² + 2ab + b².
  • The mental calculation of [(x + 1)(x - 1)]² leads to:

    • x^4 - 2x² + 1, which emphasizes the squared form of a difference of squares.
  • For (ab + 3)², the result is:

    • a²b² + 6ab + 9, also following the squared binomial formula.
  • The product of (r + s)² is expressed as:

    • r² + 2rs + s², reinforcing the expansion of the squared sum.

Difference of Squares

  • The calculation of (r - s)² results in:

    • r² - 2rs + s², aligning with the squared difference principle.
  • Evaluating (2m - 9)² produces:

    • 4m² - 36m + 81, exhibiting the expansion of a squared binomial.
  • The expression (2j + 7)(2j - 7) simplifies to:

    • 4j² - 49, confirming the difference of squares.

Additional Products

  • The correct product for (2x + 9)(x + 1) is:

    • 2x² + 11x + 9, highlighting distribution and combination of like terms.
  • The result for (z - 12)(z + 12) is:

    • z² - 144, demonstrating another example of the difference of squares.

FOIL Method

  • FOIL is an acronym to remember binomial multiplication:
    • First, Outside, Inside, Last are the steps for accurate multiplication of two binomials.

Key Concepts of Squaring Binomials

  • A binomial squared involves three steps:
    • Square the first term, double the product of both terms, and square the last term.
  • Binomials differing only by sign lead to the difference of squares, resulting in the equation: a² - b².

Studying That Suits You

Use AI to generate personalized quizzes and flashcards to suit your learning preferences.

Quiz Team

Description

Explore the fundamentals of algebra with these flashcards focused on the F.O.I.L method and special cases. Each flashcard contains key terms and definitions to enhance your understanding of polynomial multiplication. Perfect for students looking to reinforce their algebra skills!

More Like This

Algebra Class Products and Factoring
23 questions
Use Quizgecko on...
Browser
Browser