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25 April, 05:14

Expand and simplify (k-3) ^7

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Answers (2)
  1. 25 April, 07:20
    0
    (k - 3) ⁷

    (k - 3) (k - 3) (k - 3) (k - 3) (k - 3) (k - 3) (k - 3)

    (k (k - 3) - 3 (k - 3)) (k (k - 3) - 3 (k - 3)) (k (k - 3) - 3 (k - 3)) (k - 3)

    (k (k) - k (3) - 3 (k) - 3 (-3)) (k (k) - k (3) - 3 (k) - 3 (-3)) (k (k) - k (3) - 3 (k) - 3 (-3)) (k - 3)

    (k² - 3k - 3k + 9) (k² - 3k - 3k + 9) (k² - 3k - 3k + 9) (k - 3)

    (k² - 6k + 9) (k² - 6k + 9) (k² - 6k + 9) (k - 3)

    (k² (k² - 6k + 9) - 6k (k² - 6k + 9) + 9 (k² - 6k + 9)) (k² (k - 3) - 6k (k - 3) + 9 (k - 3))

    (k² (k²) - k² (6k) + k² (9) - 6k (k²) - 6k (-6k) - 6k (9) + 9 (k²) - 9 (6k) + 9 (9)) (k² (k) - k² (3) - 6k (k) - 6k (-3) + 9 (k) - 9 (3))

    (k⁴ - 6k³ + 9k² - 6k³ + 36k² - 54k + 9k² - 54k + 81) (k³ - 3k² - 6k² + 18k + 9k - 27)

    (k⁴ - 6k³ - 6k³ + 9k² + 36k² + 9k² - 54k - 54k - 81) (k³ - 9k² + 27k - 27)

    (k⁴ - 12k³ + 54k² - 108k - 81) (k³ - 9k² + 27k - 27)

    k⁴ (k³ - 9k² + 27k - 27) - 12k³ (k³ - 9k² + 27k² - 27) + 54k² (k³ - 9k² + 27k² - 27) - 108k (k³ - 9k² + 27k - 27) - 81 (k³ - 9k² + 27k - 27)

    k⁴ (k³) - k⁴ (9k²) + k⁴ (27k) - k⁴ (27) - 12k³ (k³) - 12k³ (-9k²) - 12k³ (27k) - 12k³ (-27) + 54k² (k³) - 54k² (9k²) + 54k² (27k) - 54k² (27) - 108k (k³) - 108k (9k²) - 108k (27k) - 108k (-27) - 81 (k³) - 81 (-9k²) - 81 (27k) - 81 (-27)

    k⁷ - 9k⁶ + 27k⁵ - 27k⁴ - 12k⁶ + 108k⁵ - 324k⁴ + 324k³ + 54k⁵ - 486k⁴ + 1458k³ - 1458k² - 108k⁴ - 972k³ - 2916k² + 2916k - 81k³ + 729k² - 2187k + 2187

    k⁷ - 9k⁶ - 12k⁶ + 27k⁵ + 108k⁵ + 54k⁵ - 27k⁴ - 324k⁴ - 486k⁴ - 108k⁴ + 324k³ + 1458k³ - 972k³ - 81k³ - 1458k² - 2196k² + 729k² + 2916k - 2187k + 2187

    k⁷ - 21k⁶ + 189k⁵ - 945k⁴ + 729k³ - 2925k² + 729k + 2187
  2. 25 April, 07:47
    0
    There are a couple of ways you can solve this. You can write it out like

    (K-3) (K-3) (K-3) (K-3) (K-3) (K-3) (K-3)

    And pretty much use the foil method

    Or you can use the binomial theorem (google it if you dont know)

    The solution should be:

    (K^7) - 21 (k^6) + 189 (k^5) - 945 (k^4) + 2835 (k^3) - 5103 (k^2) + 5103k - 2187
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