Podcast
Questions and Answers
What method should be used to find the product of 2 binomials?
What method should be used to find the product of 2 binomials?
What is the result of applying the sum and difference of 2 terms formula to (A+B)(A-B)?
What is the result of applying the sum and difference of 2 terms formula to (A+B)(A-B)?
A^2 - B^2
What is the square of a binomial for (A+B)^2?
What is the square of a binomial for (A+B)^2?
A^2 + 2AB + B^2
What is the formula for the sum or difference of two cubes?
What is the formula for the sum or difference of two cubes?
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How do you factor perfect square trinomials?
How do you factor perfect square trinomials?
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What is the result of the difference of two squares formula, A^2 - B^2?
What is the result of the difference of two squares formula, A^2 - B^2?
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The sum of two squares can always be factored.
The sum of two squares can always be factored.
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The order of factoring involves finding the ___ first.
The order of factoring involves finding the ___ first.
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What is the product rule for exponents?
What is the product rule for exponents?
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What is the power rule for exponents?
What is the power rule for exponents?
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What does the quotients to powers rule state?
What does the quotients to powers rule state?
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Study Notes
Product of 2 Binomials
- Use FOIL (First, Outside, Inside, Last) to expand the expression: (3x + 2)(4x + 5).
Sum and Difference of 2 Terms
- Expressed as (A + B)(A - B).
- Results in A² - B², a difference of squares.
Square of a Binomial
- For (A + B)²: expands to A² + 2AB + B².
- For (A - B)²: expands to A² - 2AB + B².
Sum or Difference of Two Cubes
- Formula: A³ ± B³ = (A ± B)(A² ± AB + B²).
- Remember the acronym SOAP (Same, Opposite, Always Positive).
Factor Perfect Square Trinomials
- Forms: A² ± 2AB + B².
- Factors as (A ± B)², where the sign matches the first sign in the trinomial.
Difference of Two Squares
- Expression: A² - B².
- Factors into (A + B)(A - B), showcasing a key algebraic identity.
Sum of Two Squares
- The expression A² + B² cannot be factored over the reals; it is considered prime.
Order of Factoring
- Start with the Greatest Common Factor (GCF).
- Identify the number of terms to determine factoring strategy, such as perfect square trinomials, or using the grouping method.
Product Rule for Exponents
- When multiplying like bases: b^m × b^n = b^(m+n).
Power Rule (Powers to Powers)
- When raising a power to another power: (b^m)ⁿ = b^(m*n).
Quotients to Powers Rule for Exponents
- For division of like bases raised to a power: (a/b)ⁿ = aⁿ/bⁿ.
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Description
Explore the various special products in algebra with this quiz. These products include the product of two binomials, sum and difference of two terms, and the square of a binomial, among others. Test your understanding and enhance your skills in using these important formulas.
