Special Products in Algebra

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Questions and Answers

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)?

A^2 - 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?

<p>A^3 +/- B^3 = (A +/- B)(A^2 +/- AB + B^2)</p> Signup and view all the answers

How do you factor perfect square trinomials?

<p>A^2 +/- 2AB + B^2 = (A +/- B)^2</p> Signup and view all the answers

What is the result of the difference of two squares formula, A^2 - B^2?

<p>(A+B)(A-B)</p> Signup and view all the answers

The sum of two squares can always be factored.

<p>False (B)</p> Signup and view all the answers

The order of factoring involves finding the ___ first.

<p>GCF</p> Signup and view all the answers

What is the product rule for exponents?

<p>b^m x b^n = b^(m+n)</p> Signup and view all the answers

What is the power rule for exponents?

<p>(b^m)^n = b^(mn)</p> Signup and view all the answers

What does the quotients to powers rule state?

<p>(a/b)^n = a^n/b^n</p> Signup and view all the answers

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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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