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12 April, 02:47

Simplify the expressions. Show your work.

1. (3x (4x4 - 5x)

2. (5x4 - 3x3 + 6x) - (3x3 + 11x2 - 8x)

3. (x - 2) (3x-4)

4. (x + 6) 2

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Answers (1)
  1. 12 April, 03:06
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    1. (3x (4x^4 - 5x))

    Steps

    Distributive Formula: a (b + c) = ab + ac

    a = 3x

    b = 4x^4

    c = - 5x

    = 3x * 4x^4 + 3x (-5x)

    = 3x * 4x^4 - 3x * 5x

    Simplify,

    = 12x^5 - 15x^2

    2. (5x^4 - 3x^3 + 6x) - (3x^3 + 11x^2 - 8x)

    Steps

    Remove the parentheses: (a) = a

    = 5x^4 - 3x^3 + 6x - (3x^3 + 11x^2 - 8x)

    - (3x^3 + 11x^2 - 8x) : - 3x^3 - 11x^2 + 8x

    = 5x^4 - 3x^3 + 6x - 3x^3 - 11x^2 + 8x

    Then simplify,

    = 5x^4 - 6x^3 - 11x^2 + 14x

    3. (x - 2) (3x - 4)

    Steps

    Distributive formula: (a + b) (c + d) = ac + ad + bc + bd

    a = x

    b = - 2

    c = 3x

    d = - 4

    = x * 3x + x (-4) - 2 * 3x - 2 (-4)

    = x * 3x - x * 4 - 2 * 3x + 2 * 4

    Then simplify,

    = 3x^2 - 10x + 8

    4. (x + 6) ^2

    Steps

    Formula: (a + b) ^2 = a^2 + 2ab + b^2

    a = x

    b = 6

    = x^2 + 2x * 6 + 6^2

    Simplify,

    = x^2 + 12x + 36
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