SLIDE SHOW INSTRUCTIONS This presentation is completely under your control. This lesson will show only one step at a time, to see the next step you must press a key. to see the next step you must press a key. (Actual names written on a key are in green) TO STOP THE SLIDE SHOW: press ‘escape’ (Esc, top left of keyboard) TO MOVE FORWARD: press the “spacebar” or Enter (PageDn, , , also work) TO MOVE BACKWARD: press the  key (PageUp, or  also work)

Polynomial Multiplication C opyright©1999 Lynda Greene

The FOIL Multiplication Method

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)(x 2 + 2x -3) cannot use FOIL Three terms: Trinomial

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

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

7 (2x + 3)(x + 2) F 2x 2 F:first times first O + 4x O:outer times outer 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: 2x 2 + 7x + 6

8 (3x - 4)(2x + 1) F 6x 2 F:first times first O + 3x O:outer times outer 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: 6x 2 - 5x - 4

9 (x - 6) (x + 6) F x 2 F:first times first O + 6x O:outer times outer 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: x

FOIL Practice Problems: (Hit enter to see the answers) 1)(x + 7)(x – 3) 2)(x – 2)(x – 5) 3) (x + 2y)(3x + y) 4)(x + 3)(x – 3) 5)(2 + x)(3 + x) Answers: 1) x2 x2 + 4x – 21 2) x2 x2 – 7x ) 3x 2 + 7xy + 2y 2 4) x2 x ) 6 + 5x + x2x2

End of Tutorial Go to for more great math tutorials for your home computer Questions? send to: