Special Products in Algebra

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?

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

How do you factor perfect square trinomials?

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

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

(A+B)(A-B) Signup and view all the answers

The sum of two squares can always be factored.

False Signup and view all the answers

The order of factoring involves finding the ___ first.

GCF Signup and view all the answers

What is the product rule for exponents?

b^m x b^n = b^(m+n) Signup and view all the answers

What is the power rule for exponents?

(b^m)^n = b^(mn) Signup and view all the answers

What does the quotients to powers rule state?

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

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.

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.