If 3x – 2y=5 then, prove that 27x^3 – 8y^3 – 54x^2y + 36xy^2 = 125 ​

Question

If 3x – 2y=5 then, prove that
27x^3 – 8y^3 – 54x^2y + 36xy^2 = 125

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Mia 2 weeks 2021-10-07T15:54:26+00:00 2 Answers 0

Answers ( )

    0
    2021-10-07T15:55:49+00:00

    Answer:

    see explanation

    Step-by-step explanation:

    Using the expansion

    (a – b)³ = a³ – b³ – 3ab(a – b) on the left side

    with a = 3x and b = 2y, then

    (3x – 2y)³

    = (3x)³ – (2y)³ – 3(3x)(2y)(3x – 2y), that is

    = 27x³ – 8y³ – 18xy(3x – 2y) ← distribute

    = 27x³ – 8y³ – 54x²y + 36xy²

    Thus given

    3x – 2y = 5 ← cube both sides

    (3x – 2y)³ = 5³, hence

    27x³ – 8y³ – 54x²y + 36xy² = 125 ← as required

    0
    2021-10-07T15:56:16+00:00

    Step-by-step explanation:

    (3x-2y)³=5³

    (3x)³-3(3x)².2y+3.3x.(2y)²-(2y)³=125

    27x³-54x²y+36y²x-8y³=125

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45:7+7-4:2-5:5*4+35:2 =? ( )