b)
3⁸⁰ - 2 x 3⁷⁹ - 2 x 3⁷⁸ = 3⁷⁸ ( 3² - 2 x 3 - 2 x 1 ) = 3⁷⁸ x ( 9 - 6 - 2 ) = 3⁷⁸ x 1 = 3⁷⁸
c)
2¹⁰ - 2⁹ - 2⁸ - 2⁷ - 2⁶ - 2⁵ - 2⁴ - 2³ - 2² - 2¹ =
= ( 2¹⁰ - 2⁹ ) - ( 2⁸ - 2⁷ ) - ( 2⁶ - 2⁵ ) - ( 2⁴ - 2³ ) - ( 2² - 2 ) =
= 2⁹ ( 2 - 1 ) - 2⁷ ( 2 - 1 ) - 2⁵ ( 2 - 1 ) - 2³ ( 2 - 1) - 2 ( 2 - 1) =
= 2⁹ x 1 - 2⁷ x 1 - 2⁵ x 1 - 2³ x 1 - 2 x 1 =
= 2⁷ ( 2² - 1 ) - 2³ ( 2² - 1) - 2 =
= 2⁷ x ( 4 - 1) - 2³ x ( 4 - 1) - 2 =
= 2⁷ x 3 - 2³ x 3 - 2 =
= 2³ x 3 ( 2⁴ - 1 ) - 2 =
= 8 x 3 x ( 16 - 1 ) - 2 =
= 24 x 15 - 2 =
= 360 - 2 =
= 358
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d)
2³ⁿ⁺¹ + 4ⁿ⁺¹ x 2ⁿ⁺² - 8ⁿ⁺¹ = 2³ⁿ x 2 + 2²ⁿ x 2² x 2ⁿ x 2² - 2³ⁿ x 2³ =
= 2³ⁿ x 2 + 2³ⁿ x 2⁴ - 2³ⁿ x 2³ =
= 2³ⁿ x 2 ( 1 + 2³- 2² ) =
= 2³ⁿ x 2 x ( 9 - 4 ) =
= 2³ⁿ x 2 x 5 =
= 2³ⁿ x 10
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e) 4ⁿ ⁺¹ - 2²ⁿ = 2² ⁽ ⁿ ⁺ ¹ ⁾ - 2²ⁿ = 2²ⁿ x ( 2² - 1 ) = 4ⁿ x ( 4 - 1 ) = 4ⁿ x 3
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f) 9 x 25ⁿ - 5²ⁿ = 9 x 25ⁿ - 25ⁿ = 25ⁿ x ( 9 - 1 ) = 25ⁿ x 8
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g)
4⁵ - 4⁴ x 3 - 4³ x 3 - 4² x 3 - 4 x 3 =
= ( 4⁵ - 4⁴ x 3 ) - ( 4³ x 3 - 4² x 3 ) - 12 =
= 4⁴ x ( 4 - 3 ) - 4² x 3 x ( 4 - 1 ) - 12 =
= 4⁴ x 1 - 4² x 3 x 3 - 12 =
= 4² x ( 4² - 9 ) - 12 =
= 4² x ( 16 - 9 ) - 12 =
= 16 x 7 - 12 =
= 112 - 12 =
= 100
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