M308 Advanced Algebra 2 Chapter R Part B Review

Vocabulary flashcards covering factoring techniques, rational expressions, domain rules, and complex fractions from the M308 Chapter R Part B lecture notes.

GCF (Greatest Common Factor)

The first technique to always look for when factoring algebraic expressions.

Domain

The allowable $x$-values for a given function.

Sum of Cubes Formula

$$a^3 + b^3 = (a + b)(a^2 - ab + b^2)$$

Difference of Cubes Formula

$$a^3 - b^3 = (a - b)(a^2 + ab + b^2)$$

SOAP

A mnemonic acronym for remembering the sign pattern when factoring sum and difference of cubes: Same, Opposite, Always Positive.

First Step in Simplifying Rational Expressions

Factor first whenever possible.

Least Common Denominator (LCD)

A common denominator constructed by writing denominators as a product of prime factors and forming a product of all different factors using their highest exponents.

Subtraction Rule for Rational Expressions

When subtracting rational expressions, distribute the negative sign across the numerator.

Numerator and Denominator Factoring Guidance

Factor the denominator first, and do not factor the numerator until the end of the simplification.

Complex Fraction Simplification Steps

Step 1: Find the LCM. Step 2: Multiply everybody by the LCM.