THE FOIL METHOD <ul><li>ALGEBRA I </li></ul><ul><li>DECEMBER 18, 2008 </li></ul><ul><li>A NEW AND EXCITING WAY TO MULTIPLY...
Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word...
Objective The student will be able to: multiply two polynomials using the FOIL method.
1)  Multiply. (2x + 3)(5x + 8) <ul><li>Using the distributive property, multiply  2x (5x + 8) +  3 (5x + 8). </li></ul><ul...
The FOIL method is only used when you multiply 2 binomials. It tells you which terms to multiply.  2)  Use the FOIL method...
(x + 3)(x + 7).  F  tells you to multiply the  FIRST  terms of each binomial. <ul><li>x 2 </li></ul>
(x + 3)(x + 7).  O  tells you to multiply the  OUTER  terms of each binomial. <ul><li>x 2   +   7x </li></ul>
(x + 3)(x + 7).  I  tells you to multiply the  INNER  terms of each binomial. x 2  + 7x  +   3x
(x + 3)(x + 7).  L  tells you to multiply the  LAST  terms of each binomial. <ul><li>x 2  + 7x + 3x  + 21 </li></ul><ul><l...
Remember, FOIL reminds you to multiply the: <ul><li>F irst terms </li></ul><ul><li>O uter terms </li></ul><ul><li>I nner t...
3)  Multiply. (x + 5)(x + 4) <ul><li>First terms:  x 2 </li></ul><ul><li>Outer terms:  + 4x </li></ul><ul><li>Inner terms:...
3)  Multiply. (3x - 5)(5x + 2) <ul><li>First terms:  15x 2 </li></ul><ul><li>Outer terms:  + 6x </li></ul><ul><li>Inner te...
4)  Multiply (7p - 2)(3p - 4) <ul><li>First terms:  21p 2 </li></ul><ul><li>Outer terms:  - 28p </li></ul><ul><li>Inner te...
4)  Multiply (5x - 2)(5x + 2) <ul><li>First terms:  25x 2 </li></ul><ul><li>Outer terms:  10x </li></ul><ul><li>Inner term...
ASSESSMENT TIME <ul><li>NOW THAT WE DID FOUR EXERCISES, DID ANYBODY GET THEM ALL CORRECT? </li></ul><ul><li>HOW MANY WOULD...
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  1. 1. THE FOIL METHOD <ul><li>ALGEBRA I </li></ul><ul><li>DECEMBER 18, 2008 </li></ul><ul><li>A NEW AND EXCITING WAY TO MULTIPLY BINOMIALS </li></ul><ul><li>INSTRUCTOR – TONY AMATO </li></ul><ul><li>CA. CONTENT STANDARD 10 </li></ul>
  2. 2. Students add, subtract, multiply, and divide monomials and polynomials. Students solve multi-step problems, including word problems, by using these techniques CALIFORNIA CONTENT STANDARD – 10
  3. 3. Objective The student will be able to: multiply two polynomials using the FOIL method.
  4. 4. 1) Multiply. (2x + 3)(5x + 8) <ul><li>Using the distributive property, multiply 2x (5x + 8) + 3 (5x + 8). </li></ul><ul><li>10x 2 + 16x + 15x + 24 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>10x 2 + 31x + 24 </li></ul><ul><li>A shortcut of the distributive property is called the FOIL method. </li></ul>
  5. 5. The FOIL method is only used when you multiply 2 binomials. It tells you which terms to multiply. 2) Use the FOIL method to multiply the following binomials: (x + 3)(x + 7).
  6. 6. (x + 3)(x + 7). F tells you to multiply the FIRST terms of each binomial. <ul><li>x 2 </li></ul>
  7. 7. (x + 3)(x + 7). O tells you to multiply the OUTER terms of each binomial. <ul><li>x 2 + 7x </li></ul>
  8. 8. (x + 3)(x + 7). I tells you to multiply the INNER terms of each binomial. x 2 + 7x + 3x
  9. 9. (x + 3)(x + 7). L tells you to multiply the LAST terms of each binomial. <ul><li>x 2 + 7x + 3x + 21 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>x 2 + 10x + 21 </li></ul>
  10. 10. Remember, FOIL reminds you to multiply the: <ul><li>F irst terms </li></ul><ul><li>O uter terms </li></ul><ul><li>I nner terms </li></ul><ul><li>L ast terms </li></ul>
  11. 11. 3) Multiply. (x + 5)(x + 4) <ul><li>First terms: x 2 </li></ul><ul><li>Outer terms: + 4x </li></ul><ul><li>Inner terms: +5x </li></ul><ul><li>Last terms: +20 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>x 2 + 9x + 20 </li></ul>
  12. 12. 3) Multiply. (3x - 5)(5x + 2) <ul><li>First terms: 15x 2 </li></ul><ul><li>Outer terms: + 6x </li></ul><ul><li>Inner terms: -25x </li></ul><ul><li>Last terms: -10 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>15x 2 - 19x - 10 </li></ul>
  13. 13. 4) Multiply (7p - 2)(3p - 4) <ul><li>First terms: 21p 2 </li></ul><ul><li>Outer terms: - 28p </li></ul><ul><li>Inner terms: - 6p </li></ul><ul><li>Last terms: + 8 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>21p 2 - 34p + 8 </li></ul>
  14. 14. 4) Multiply (5x - 2)(5x + 2) <ul><li>First terms: 25x 2 </li></ul><ul><li>Outer terms: 10x </li></ul><ul><li>Inner terms: - 10x </li></ul><ul><li>Last terms: - 4 </li></ul><ul><li>Combine like terms. </li></ul><ul><li>25x 2 + 0x – 4, now simplify </li></ul><ul><li>25x 2 – 4 </li></ul>
  15. 15. ASSESSMENT TIME <ul><li>NOW THAT WE DID FOUR EXERCISES, DID ANYBODY GET THEM ALL CORRECT? </li></ul><ul><li>HOW MANY WOULD LIKE TO REVIEW THE ENTIRE CONCEPT OF FOIL? </li></ul><ul><li>WHO NEEDS FURTHER REVIEW OF MULTIPLYING VARIABLES AND COEFFICIENTS? </li></ul><ul><li>WHO WOULD LIKE TO SEE MORE EXAMPLES OF FOIL? </li></ul>

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