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ADDING, SUBTRACTING, & MULTIPLYING POLYNOMIALS
JOURNAL ENTRY ERROR ANALYSIS <ul><li>A student simplified 6a³ -a³ and got a 6 as a result.  Write an explanation of the st...
CHALLANGE <ul><li>A 35-centimeter stick is cut into three pieces so that the two end pieces are each equal in length to on...
 
MULTIPLYING POLYNOMIALS <ul><li>3a(6b + 7) </li></ul><ul><li>(3a)(6b) + (3a)(7) </li></ul><ul><li>18ab + 21a </li></ul><ul...
YOUR TURN <ul><li>-4a²(-2a² + 3ab – 2b + 5) </li></ul>
MULTIPLYING BINOMIALS <ul><li>(x + 2)(x + 3) </li></ul><ul><li>x(x+ 3) + 2(x + 3) </li></ul><ul><li>(x)( x)+ (x)(3) + 2(x)...
FOIL METHOD <ul><li>(x + 3)(x + 2)  +  +  + </li></ul><ul><li>x² + 2x + 3x + 6 </li></ul><ul><li>x² + 5x+ 6 </li></ul>firs...
YOUR TURN – USE FOIL METHOD <ul><li>1. (x + 4)(x  -  3)  2. (2x + 2)(x + 6) </li></ul><ul><li>3. (3ab² + b)(-2ab² - b)  4....
FOIL <ul><li>1.  (x + 4)(x – 4)  2.  (x + 3)(x – 3) </li></ul><ul><li>3.  (3y – 1)(3y + 1)  4.  (2x² + 3)(2x² - 3) </li></...
FOIL <ul><li>1.(y + 1)(y + 1)  2. (x + 2)²  </li></ul><ul><li>3.  (2x - 3)²  4. .(y² + 1)²  </li></ul><ul><li>5.(2x – y)² ...
SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS! <ul><li>Sum & Difference  (S&D): </li></ul><ul><l...
MULTIPLYING POLYNOMIALS: VERTICALLY <ul><li>(-x 2  + 2x + 4)(x – 3)= </li></ul><ul><li>-x 2  + 2x + 4 *  x – 3 </li></ul><...
MULTIPLYING POLYNOMIALS : HORIZONTALLY <ul><li>(x – 3)(3x 2  – 2x – 4)= </li></ul><ul><li>(x – 3)(3x 2 )  </li></ul><ul><l...
MULTIPLYING 3 BINOMIALS : <ul><li>(x – 1)(x + 4)(x + 3) =  </li></ul><ul><li>FOIL the first two:  </li></ul><ul><li>(x 2  ...
SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS! <ul><li>Sum & Difference  (S&D): </li></ul><ul><l...
LAST PATTERN <ul><li>Cube of a Binomial </li></ul><ul><li>(a + b) 3  = a 3  + 3a 2 b + 3ab 2  + b 3 </li></ul><ul><li>(a –...
EXAMPLE: <ul><li>(x + 5) 3  = </li></ul><ul><li>a = x  and b = 5 </li></ul><ul><li>x 3  + 3(x) 2 (5) + 3(x)(5) 2  + (5) 3 ...
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6 3 Add,Sub,Mult Polynomials

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Transcript of "6 3 Add,Sub,Mult Polynomials"

  1. 1. ADDING, SUBTRACTING, & MULTIPLYING POLYNOMIALS
  2. 2. JOURNAL ENTRY ERROR ANALYSIS <ul><li>A student simplified 6a³ -a³ and got a 6 as a result. Write an explanation of the student’s error using the words coefficient and like terms. </li></ul>
  3. 3. CHALLANGE <ul><li>A 35-centimeter stick is cut into three pieces so that the two end pieces are each equal in length to one-third of the middle piece. How long is each piece? </li></ul>
  4. 5. MULTIPLYING POLYNOMIALS <ul><li>3a(6b + 7) </li></ul><ul><li>(3a)(6b) + (3a)(7) </li></ul><ul><li>18ab + 21a </li></ul><ul><li>2x(3x² + x – 4) </li></ul><ul><li>(2x)(3x²) + (2x)(x) + (2x)(-4) </li></ul><ul><li>6x³ + 2x² + -8x </li></ul>
  5. 6. YOUR TURN <ul><li>-4a²(-2a² + 3ab – 2b + 5) </li></ul>
  6. 7. MULTIPLYING BINOMIALS <ul><li>(x + 2)(x + 3) </li></ul><ul><li>x(x+ 3) + 2(x + 3) </li></ul><ul><li>(x)( x)+ (x)(3) + 2(x) + 2(3) </li></ul><ul><li>x² + 3x + 2x + 6 </li></ul><ul><li>x² + 5x + 6 </li></ul>
  7. 8. FOIL METHOD <ul><li>(x + 3)(x + 2) + + + </li></ul><ul><li>x² + 2x + 3x + 6 </li></ul><ul><li>x² + 5x+ 6 </li></ul>first 2) outer (x inside last First x·x Outer x ·2 Inside 3 · x Last 3 · 2
  8. 9. YOUR TURN – USE FOIL METHOD <ul><li>1. (x + 4)(x - 3) 2. (2x + 2)(x + 6) </li></ul><ul><li>3. (3ab² + b)(-2ab² - b) 4. (4xy + 3)(2x²y + 1) </li></ul>
  9. 10. FOIL <ul><li>1. (x + 4)(x – 4) 2. (x + 3)(x – 3) </li></ul><ul><li>3. (3y – 1)(3y + 1) 4. (2x² + 3)(2x² - 3) </li></ul><ul><li>5. (2x +y) (2x -y) 6. (x²y - 2)(x²y + 3) </li></ul>
  10. 11. FOIL <ul><li>1.(y + 1)(y + 1) 2. (x + 2)² </li></ul><ul><li>3. (2x - 3)² 4. .(y² + 1)² </li></ul><ul><li>5.(2x – y)² 6. .(2y² - 2x)² </li></ul>
  11. 12. SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS! <ul><li>Sum & Difference (S&D): </li></ul><ul><li>(a + b)(a – b) = a 2 – b 2 </li></ul><ul><li>Example: (x + 3)(x – 3) = x 2 – 9 </li></ul><ul><li>Square of Binomial: </li></ul><ul><li>(a + b) 2 = a 2 + 2ab + b 2 </li></ul><ul><li>(a - b) 2 = a 2 – 2ab + b 2 </li></ul>
  12. 13. MULTIPLYING POLYNOMIALS: VERTICALLY <ul><li>(-x 2 + 2x + 4)(x – 3)= </li></ul><ul><li>-x 2 + 2x + 4 * x – 3 </li></ul><ul><li> 3x 2 – 6x – 12 -x 3 + 2x 2 + 4x -x 3 + 5x 2 – 2x – 12 </li></ul>
  13. 14. MULTIPLYING POLYNOMIALS : HORIZONTALLY <ul><li>(x – 3)(3x 2 – 2x – 4)= </li></ul><ul><li>(x – 3)(3x 2 ) </li></ul><ul><li>+ (x – 3)(-2x) </li></ul><ul><li>+ (x – 3)(-4) = </li></ul><ul><li>(3x 3 – 9x 2 ) + (-2x 2 + 6x) + (-4x + 12) = </li></ul><ul><li>3x 3 – 9x 2 – 2x 2 + 6x – 4x +12 = </li></ul><ul><li>3x 3 – 11x 2 + 2x + 12 </li></ul>
  14. 15. MULTIPLYING 3 BINOMIALS : <ul><li>(x – 1)(x + 4)(x + 3) = </li></ul><ul><li>FOIL the first two: </li></ul><ul><li>(x 2 – x +4x – 4)(x + 3) = </li></ul><ul><li>(x 2 + 3x – 4)(x + 3) = </li></ul><ul><li>Then multiply the trinomial by the binomial </li></ul><ul><li>(x 2 + 3x – 4)(x) + (x 2 + 3x – 4)(3) = </li></ul><ul><li>(x 3 + 3x 2 – 4x) + (3x 2 + 9x – 12) = </li></ul><ul><li>x 3 + 6x 2 + 5x - 12 </li></ul>
  15. 16. SOME BINOMIAL PRODUCTS APPEAR SO MUCH WE NEED TO RECOGNIZE THE PATTERNS! <ul><li>Sum & Difference (S&D): </li></ul><ul><li>(a + b)(a – b) = a 2 – b 2 </li></ul><ul><li>Example: (x + 3)(x – 3) = x 2 – 9 </li></ul><ul><li>Square of Binomial: </li></ul><ul><li>(a + b) 2 = a 2 + 2ab + b 2 </li></ul><ul><li>(a - b) 2 = a 2 – 2ab + b 2 </li></ul>
  16. 17. LAST PATTERN <ul><li>Cube of a Binomial </li></ul><ul><li>(a + b) 3 = a 3 + 3a 2 b + 3ab 2 + b 3 </li></ul><ul><li>(a – b) 3 = a 3 - 3a 2 b + 3ab 2 – b 3 </li></ul>
  17. 18. EXAMPLE: <ul><li>(x + 5) 3 = </li></ul><ul><li>a = x and b = 5 </li></ul><ul><li>x 3 + 3(x) 2 (5) + 3(x)(5) 2 + (5) 3 = </li></ul><ul><li>x 3 + 15x 2 + 75x + 125 </li></ul>
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