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?
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What is the product of [(x + 1)(x - 1)]^2?
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What is the product of (ab + 3)^2?
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What is the product of (r + s)^2?
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What is the correct product of (a + 8)(b + 3)?
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What is the product of (r - s)^2?
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What is the product of (2m - 9)^2?
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What is the product of (2j + 7)(2j - 7)?
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What is the correct product of (2x + 9)(x + 1)?
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What is the product of (z - 12)(z + 12)?
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What does FOIL stand for?
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How is a binomial squared calculated?
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What results when binomials differ only by the sign between the terms?
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Study Notes
Binomials
- A binomial is defined as a polynomial with two terms.
Products of Binomials
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The mental product of (ab + 3)(ab - 3) results in:
- a²b² - 9, showcasing the difference of squares.
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The product of (j + 7)(k - 5) simplifies to:
- jk - 5j + 7k - 35, demonstrating distribution.
Squaring Binomials
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Squaring (n + 7) provides:
- n² + 14n + 49, derived from the formula (a + b)² = a² + 2ab + b².
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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.
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For (ab + 3)², the result is:
- a²b² + 6ab + 9, also following the squared binomial formula.
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The product of (r + s)² is expressed as:
- r² + 2rs + s², reinforcing the expansion of the squared sum.
Difference of Squares
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The calculation of (r - s)² results in:
- r² - 2rs + s², aligning with the squared difference principle.
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Evaluating (2m - 9)² produces:
- 4m² - 36m + 81, exhibiting the expansion of a squared binomial.
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The expression (2j + 7)(2j - 7) simplifies to:
- 4j² - 49, confirming the difference of squares.
Additional Products
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The correct product for (2x + 9)(x + 1) is:
- 2x² + 11x + 9, highlighting distribution and combination of like terms.
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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.
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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!
