Find the value of 373 using the identity (x − y)3 = x3 − 3x2y + 3xy2 − y3. Show all work. Hint: 373 = (40 − 3)3; therefore

Question

Find the value of 373 using the identity (x − y)3 = x3 − 3x2y + 3xy2 − y3. Show all work.

Hint: 373 = (40 − 3)3; therefore, x = 40 and y = 3.

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Ngọc Diệp 4 years 2021-08-09T10:52:52+00:00 1 Answers 20 views 0

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  1. Delwyn
    0
    2021-08-09T10:54:40+00:00
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    Answer:

    37^3 = 50653

    Step-by-step explanation:

    Given

    (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

    Required

    Find 37^3

    Express 37 as 40 – 3

    So, we have:

    37^3 = (40 - 3)^3

    Compare to (x -y)^3

    x = 40\ and\ y = 3

    Substitute 40 for x and 3 for y in (x - y)^3 = x^3 - 3x^2y + 3xy^2 - y^3

    (40 - 3)^3 = 40^3 - 3*40^2*3 + 3*40*3^2 - 3^3

    Evaluate all exponents

    (40 - 3)^3 = 64000 - 3*1600*3 + 3*40*9 - 27

    Evaluate all products

    (40 - 3)^3 = 64000 - 14400 + 1080 - 27

    (40 - 3)^3 = 50653

    Hence:

    37^3 = 50653

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