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cubbieben
cubbieben asked in Science & MathematicsMathematics · 9 years ago

What is the expanded form of (2a - 3b)^6? Please show step by step.?

1 Answer

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  • Dragon.Jade
    Lv 7
    9 years ago
    Favorite Answer

    Hello,

    Just make use of Pascal's Triangle:

    1

    1 1

    1 2 1

    1 3 3 1

    1 4 6 4 1

    1 5 10 10 5 1

    1 6 15 20 15 6 1

    Thus,

    (x + y)⁶ = x⁶ + 6x⁵y + 15x⁴y² + 20x³y³ + 15x²y⁴ + 6xy⁵ + y⁶

    Using x=2a and y=-3b:

    (2a - 3b)⁶

      = (2a)⁶ + 6(2a)⁵(-3b) + 15(2a)⁴(-3b)² + 20(2a)³(-3b)³ + 15(2a)²(-3b)⁴ + 6(2a)(-3b)⁵ + (-3b)⁶

      = 64a⁶ - 576a⁵b + 2160a⁴b² - 4320a³b³ + 4860a²b⁴ - 2916ab⁵ + 729b⁶

    Regards,

    Dragon.Jade :-)

    Source(s): http://en.wikipedia.org/wiki/Pascal%27s_triangle
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