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Combining like terms

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The document defines exponents and provides examples of multiplying and combining like terms with exponents. It explains that to multiply terms, you multiply the coefficients and add the exponents of like terms. It provides examples of multiplying, combining, and dividing like terms with variables and exponents.

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TERMS… Define Term : A number times a letter raised to an exponent # x ² Coefficient : The number Variable : The letter Examples: 7x², -3xy³, 12
I've Got The Power!! Review of Exponents… 4 ³ The 4 is the BASE The 3 is the EXPONENT / POWER You multiple the base by ITSELF the exponent times… So, 4 times itself 3 times… 4³ = (4)(4)(4)… Now, if we have numbers, we can solve so 4³ = 64
Exponents Cont. What if we have letters??? x ³ = xxx y² = yy (2)²x 4 y 5 = (2)(2)xxxxyyyyy Practice: Z 6 = x²y³ = (5) 3 x 7 y 2 =
Let's Go The Other Way… (3)(3)(3)(3) = 3 4 ccccccc = c 7 Rrssst = r 2 s 3 t (2)(2)xxxyyzzzz = 2 2 x 3 y 2 z 4 Your Turn……. Go to Workbook 2, page
Multiplying Terms Multiply BIG – Add SMALL Multiply the COEFFICIENTS and Add the EXPONENTS 1. (2x)(4x) …..Multiply 2 and 4 Add your exponents 1 and 1 So, you get 8x 2
More Multiplying Terms Remember: Multiply Coefficients (big numbers) and Add Exponents (little numbers) Practice: 1.  (-11m 4 )(-6m 3 p 2 ) = 66m 7 p 2 2.  (-2f 3 )(-3f 4 s 3 ) = 6f 7 s 3 3.  (10v 2 )(v 2 k 6 ) = 10v 4 k 6 4.  (-5 l 6 h 4 )(10 l 6 h 6 ) = -50 l 12 h 10
5.  (-5f 2 )(f 3 c 3 ) = 6.  (-12b 3 z 4 )(-11b 5 z 5 ) = 7.  (7w 6 m 2 )(9w 3 m 3 ) = 8.  (-6t 5 )(-5t 6 x 3 ) = 9.  (4r 5 e 4 )(3r 4 ) = 10.  (2g 3 )(-3g 6 u 6 ) = You practice these independently!!
Like Terms Like Terms Must Have same variable and exponent Example 7x ³ 4x³ -5x³ 2,984x³ 8xxx -65xxx x³
Match The Like Terms 5c c -8x ² 4xx 68 6x ³y² 123 - ⅓xxxyy 9x ³y² 4a 4 - ⅞ aaaa
Combine Like Terms Adding and Subtracting Terms You Can Only Add or Subtract LIKE TERMS Real Life Example: + 3 = 5 BUT…. 2 + 3 = 2 + 3 You can NOT add Christmas Trees and Ornaments… They are DIFFERENT !!
Let’s Practice… 4x + x = -3y + 4y = 6x ³ + 3x³ - x³ = 12m² - 4m² = 2x²yz 4 + 5x²yz 4 - x²yz 4 = Complete Page 20 in Workbook 2…
Combining Like Terms Cont. MORE PRACTICE… 4x ² + 3x² 4x³ - 2x² +3x - x³ + 5x³ - x -5x + 12 + 6x - 9 3a + 5b - a + 9b - 8a
More Combining Like Terms 1.  9z 2 + 19z 2 + 13z + 11z + 18 - 2 + 3 2.  10 - 5k + 8k + 17 - 7 3.  12b 2 + 14b - 16 4.  g + 15 - 4g - 6g 5.  6a + 7a - 18a 2 + 13a 2 - 2a 3 + 8a 4 6.  3m - 17m - 1 - 16 - 15m 7.  19h 2 - 10h - 12h - 11 - 4h 2 - 5 8.  14y + 9y 2 - 2 + y 9.  6f + 14f + 11f 2 + 17f 3 - 19f + 9f + 13f 4 10.  7d - 18d
Dividing Terms Review:    28 15 48 7 30 12 What about Variables?? x 4 x 7

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Combining like terms

  • 1. TERMS… Define Term : A number times a letter raised to an exponent # x ² Coefficient : The number Variable : The letter Examples: 7x², -3xy³, 12
  • 2. I've Got The Power!! Review of Exponents… 4 ³ The 4 is the BASE The 3 is the EXPONENT / POWER You multiple the base by ITSELF the exponent times… So, 4 times itself 3 times… 4³ = (4)(4)(4)… Now, if we have numbers, we can solve so 4³ = 64
  • 3. Exponents Cont. What if we have letters??? x ³ = xxx y² = yy (2)²x 4 y 5 = (2)(2)xxxxyyyyy Practice: Z 6 = x²y³ = (5) 3 x 7 y 2 =
  • 4. Let's Go The Other Way… (3)(3)(3)(3) = 3 4 ccccccc = c 7 Rrssst = r 2 s 3 t (2)(2)xxxyyzzzz = 2 2 x 3 y 2 z 4 Your Turn……. Go to Workbook 2, page
  • 5. Multiplying Terms Multiply BIG – Add SMALL Multiply the COEFFICIENTS and Add the EXPONENTS 1. (2x)(4x) …..Multiply 2 and 4 Add your exponents 1 and 1 So, you get 8x 2
  • 6. More Multiplying Terms Remember: Multiply Coefficients (big numbers) and Add Exponents (little numbers) Practice: 1.  (-11m 4 )(-6m 3 p 2 ) = 66m 7 p 2 2.  (-2f 3 )(-3f 4 s 3 ) = 6f 7 s 3 3.  (10v 2 )(v 2 k 6 ) = 10v 4 k 6 4.  (-5 l 6 h 4 )(10 l 6 h 6 ) = -50 l 12 h 10
  • 7. 5.  (-5f 2 )(f 3 c 3 ) = 6.  (-12b 3 z 4 )(-11b 5 z 5 ) = 7.  (7w 6 m 2 )(9w 3 m 3 ) = 8.  (-6t 5 )(-5t 6 x 3 ) = 9.  (4r 5 e 4 )(3r 4 ) = 10.  (2g 3 )(-3g 6 u 6 ) = You practice these independently!!
  • 8. Like Terms Like Terms Must Have same variable and exponent Example 7x ³ 4x³ -5x³ 2,984x³ 8xxx -65xxx x³
  • 9. Match The Like Terms 5c c -8x ² 4xx 68 6x ³y² 123 - ⅓xxxyy 9x ³y² 4a 4 - ⅞ aaaa
  • 10. Combine Like Terms Adding and Subtracting Terms You Can Only Add or Subtract LIKE TERMS Real Life Example: + 3 = 5 BUT…. 2 + 3 = 2 + 3 You can NOT add Christmas Trees and Ornaments… They are DIFFERENT !!
  • 11. Let’s Practice… 4x + x = -3y + 4y = 6x ³ + 3x³ - x³ = 12m² - 4m² = 2x²yz 4 + 5x²yz 4 - x²yz 4 = Complete Page 20 in Workbook 2…
  • 12. Combining Like Terms Cont. MORE PRACTICE… 4x ² + 3x² 4x³ - 2x² +3x - x³ + 5x³ - x -5x + 12 + 6x - 9 3a + 5b - a + 9b - 8a
  • 13. More Combining Like Terms 1.  9z 2 + 19z 2 + 13z + 11z + 18 - 2 + 3 2.  10 - 5k + 8k + 17 - 7 3.  12b 2 + 14b - 16 4.  g + 15 - 4g - 6g 5.  6a + 7a - 18a 2 + 13a 2 - 2a 3 + 8a 4 6.  3m - 17m - 1 - 16 - 15m 7.  19h 2 - 10h - 12h - 11 - 4h 2 - 5 8.  14y + 9y 2 - 2 + y 9.  6f + 14f + 11f 2 + 17f 3 - 19f + 9f + 13f 4 10.  7d - 18d
  • 14. Dividing Terms Review:    28 15 48 7 30 12 What about Variables?? x 4 x 7