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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. Collect like terms and Arrange each polynomial in descending order for x <ul><li>3x²y³ + - 2xy + 3x³y² - 5x²y³ - 8xy + 4x³y² </li></ul><ul><li>Collect like terms and Arrange each polynomial in descending order for b </li></ul><ul><li>4a 3 + 7a 2 b + b 3 - 3ab 2 + b 3 - a 3 + 3a 2 b </li></ul>
4. 4. Add Polynomials Column form <ul><li>Add 3x 3 +2x 2 -x-7 and x 3 -10x 2 +8. </li></ul><ul><li>3x 3 + 2x 2 – x – 7 + x 3 – 10x 2 + 8 Line up like terms </li></ul><ul><li>4x 3 – 8x 2 – x + 1 </li></ul>
5. 5. YOU TRY <ul><li>Add 7x 3 +6x 2 + 4x + 1 and -7x 3 + 6x 2 + - 4x + 8. </li></ul><ul><li>7x 3 + 6x 2 +4x +1 </li></ul><ul><li>+ -7x 3 + 6x 2 +-4x + 8 Line up like terms </li></ul><ul><li>12x 2 + 9 </li></ul><ul><li>12x 2 + 9 </li></ul>
6. 6. HORIZONTAL FORMAT : COMBINE LIKE TERMS <ul><li>(8x 3 – 3x 2 – 2x + 9) +(-2x 3 - 6x 2 +x - 1)= </li></ul><ul><li>(8x 3 – 2x 3 )+(-3x 2 – 6x 2 )+(-2x + x) + (9 – 1)= </li></ul><ul><li>6x 3 + -9x 2 + -x + 8 = </li></ul><ul><li>6x 3 – 9x 2 – x + 8 </li></ul>
7. 7. YOUR TURN <ul><li>(7x 3 – 4x 2 – 4x + 3) +(- 2x 2 -3x 3 +3x - 5)= </li></ul><ul><li>(7x 3 – 3x 3 )+(-4x 2 – 2x 2 )+(-4x + 3x) + (3 – 5)= </li></ul><ul><li>4x 3 + -6x 2 + x + -2 = </li></ul><ul><li>4x 3 – 6x 2 + x + -2 </li></ul>
8. 8. Add the polynomials <ul><li>(-3cd³ + 6d² + 2cd – 1) + (-3d² + 2cd +1) </li></ul><ul><li>(9x -7x +2x² + 5) + (8x + 4x - 2x) + (2x² - 8) </li></ul><ul><li>(4x²y – 5xy + 7) + (8x²y + 7xy² + 3xy – 2) </li></ul><ul><li>(7y - 6y + 3y³ - 1) + (6y - 3y³ + 6y² + 5) </li></ul>
9. 9. Subtracting Polynomials <ul><li>To perform subtraction we add the additive inverse. </li></ul><ul><li>2 – 1 = 2 + -1, a – b = a + -b </li></ul><ul><li>What is the additive inverse of 4x² + 2x – 1 </li></ul><ul><li>-(4x² + 2x – 1)= </li></ul><ul><li>-1(4x² + 2x – 1) </li></ul><ul><li>- 4x² - 2x + 1 </li></ul>
10. 10. Find the additive inverse of <ul><li>2x² - 4 </li></ul><ul><li>5x + 3x³ - 4y + 3 </li></ul>
11. 11. Subtract Polynomials Column form <ul><li>(4x 3 y 2 +3x 2 -x-7) – (x 3 y 2 -10x 2 +8) </li></ul><ul><li>(4x 3 y 2 +3x 2 -x-7) +(-x 3 y 2 +10x 2 -8) </li></ul><ul><li>4x 3 y 2 + 3x 2 – x – 7 + - x 3 y 2 + 10x 2 - 8 Line up like terms </li></ul><ul><li> 3x 3 y 2 + 13x 2 – x - 15 </li></ul>
12. 12. YOUR TURN <ul><li>(8x 3 y 2 + 2x 2 - 3x-4) – (9x 3 y 2 - 5x 2 - 8) </li></ul><ul><li>(8x 3 y 2 + 2x 2 – 3x -4) +(-9x 3 y 2 + 5x 2 +8) </li></ul><ul><li>8x 3 y 2 + 2x 2 – 3x – 4 </li></ul><ul><li>- 9x 3 y 2 + 5x 2 + 8 Line up like terms </li></ul><ul><li> -x 3 y 2 + 7x 2 – 3x + 4 </li></ul>
13. 13. HORIZONTAL FORMAT : COMBINE LIKE TERMS <ul><li>(8x 3 – 3x 2 – 2x + 9) - (-2x 3 - 6x 2 + x - 1)= </li></ul><ul><li>(8x 3 – 3x 2 – 2x + 9) + (2x 3 + 6x 2 - x +1) </li></ul><ul><li>(8x 3 + 2x 3 )+(-3x 2 + 6x 2 )+(-2x + -x) + (9 + 1)= </li></ul><ul><li>10x 3 + 3x 2 + -3x + 10 = </li></ul><ul><li>10x 3 +3x 2 + -3x + 10 </li></ul>
14. 14. Your turn Horizontal format <ul><li>(5x² + 2) – (3x² - 8) </li></ul><ul><li>(2x – 5) – (-6x + 5) </li></ul>
15. 15. Subtract Polynomials <ul><li>(-2cd³ + 5d² + 2cd – 1) - (-3d² + 2cd +1) </li></ul><ul><li>(5x -7x +3x² + 5) - (6x - 4x - 2x) </li></ul><ul><li>(7x²y – 4xy + 7) - (3x²y + 7xy² - 3xy – 2) +(2xy + 3) </li></ul><ul><li>(8y - 6y + 2y³ - 1) - (5y + 2y³ + 6y² + 5) </li></ul>
16. 16. EXAMPLES: ADDING <ul><li>(9x 3 – 2x + 1) + (5x 2 + 12x -4) = </li></ul><ul><li>9x 3 + 5x 2 – 2x + 12x + 1 – 4 = </li></ul><ul><li>9x 3 + 5x 2 + 10x – 3 </li></ul><ul><li>(2x 2 + 3x) - (-3x 2 - x + 4)= </li></ul><ul><li>2x 2 + 3x + 3x 2 + x + -4 = </li></ul><ul><li>2x 2 + 3x 2 + 3x + x + -4 = </li></ul><ul><li>5x 2 + 4x + -4 </li></ul>