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Copyright©1999 Lynda Greene Polynomial Multiplication Copyright©1999 Lynda Greene

The FOIL Multiplication Method

multiply two binomials, such as: (x + 3)(x - 2) FOIL is a method used to multiply two binomials, such as: (x + 3)(x - 2) binomial: two terms Foil has only one use, if there are more than two terms a different method must be used. Example: (x - 2)(x2 + 2x -3) cannot use FOIL Three terms: Trinomial

(x + y)(a - 2b) FOIL is an acronym, meaning each letter stands for a word. O: stands for the outer terms F: stands for the First terms (x + y)(a - 2b) L: stands for the last terms I: stands for the inner terms

- 2bx ax - 2by + ay (x + y)(a - 2b) O F L I FOIL is the order we use to multiply these expressions O - 2bx O:outer times outer F ax F:first times first (x + y)(a - 2b) L - 2by L: last times last I + ay I:Inner times Inner It is customary to write the letters (variables) in each term in alphabetical order and to write the number (coefficient) in front.

+ 4x 2x2 + 3x + 6 (2x + 3)(x + 2) Answer: 2x2 + 7x + 6 O F L I O:outer times outer F 2x2 F:first times first (2x + 3)(x + 2) I + 3x I:Inner times Inner L + 6 L: last times last Very often the two middle terms are “like terms” and can be combined. 4x + 3x = 7x Answer: 2x2 + 7x + 6

+ 3x 6x2 - 8x - 4 (3x - 4)(2x + 1) Answer: 6x2 - 5x - 4 O F L I O:outer times outer F 6x2 F:first times first (3x - 4)(2x + 1) I - 8x I:Inner times Inner L - 4 L: last times last Very often the two middle terms are “like terms” and can be combined. 3x - 8x = -5x Answer: 6x2 - 5x - 4

+ 6x x2 - 6x - 36 (x - 6) (x + 6) Answer: x2 - 36 O F L I O:outer times outer F x2 F:first times first (x - 6) (x + 6) I - 6x I:Inner times Inner L - 36 L: last times last The answer to this kind of problem is called “the difference of two squares” The middle term always cancels out (6x – 6x = 0) Answer: x2 - 36

FOIL Practice Problems: (Hit enter to see the answers) (x + 7)(x – 3) (x – 2)(x – 5) 3) (x + 2y)(3x + y) (x + 3)(x – 3) (2 + x)(3 + x) Answers: 1) x2 + 4x – 21 2) x2 – 7x + 10 3) 3x2 + 7xy + 2y2 4) x2 - 9 5) 6 + 5x + x2

Questions? send e-mail to: lgreene1@satx.rr.com End of Tutorial Go to www.greenebox.com for more great math tutorials for your home computer Questions? send e-mail to: lgreene1@satx.rr.com