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?
- Distributive property
- Grouping
- FOIL (correct)
- Factoring
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?
How do you factor perfect square trinomials?
How do you factor perfect square trinomials?
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?
The sum of two squares can always be factored.
The sum of two squares can always be factored.
The order of factoring involves finding the ___ first.
The order of factoring involves finding the ___ first.
What is the product rule for exponents?
What is the product rule for exponents?
What is the power rule for exponents?
What is the power rule for exponents?
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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