The 3 F words Fractions, FOIL and Factoring

Fractions Addition get a common denominator Factor all denominators to help find LCD Multiply both numerator and denominator of each fraction by factors of LCD missing from the denominator add/subtract numerators denominator stays the same Subtraction change to “add the opposite” (aka keep-change-change) Multiplication cancel factors common to both numerator and denominator, multiply across and reduce Division change to “multiply by the reciprocal” (aka keep-change-flip)

FOIL First – Outer – Inner - Last (a + b)(c + d) = ac + ad + bc + bd Sum and Difference Pattern (a + b)(a – b) = a 2 – b 2 square of first term minus square of last term Square of a Binomial Pattern (a + b) 2 = a 2 + 2ab + b 2 square of first term, double the product of both terms and square of the last term

Factoring (6 common types) Common Monomial Factoring (always look for first) Factor by Grouping (4 terms) Factorable Trinomials (with shortcut) Factorable Trinomials (without shortcut) Difference of Two Squares [ a 2 – b 2 = (a + b)(a – b) ] Perfect Square Trinomials [ a 2 ± 2ab + b 2 = (a ± b) 2 ]