Polynomials

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Cubic Equation

    What is the value of 27x3 + 18x2y + 12xy2 + y3 when x = 4, y = – 8?
    1. 64
    2. 256
    3. 512
    4. 1984

 

  • Correct Answer
    Choice D. 1984
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Detailed Solution

(3x + y)3 = 27x3 + 3(3x)2y + 3(3x)y2 + y3 = 27x3 + 27x2y + 9xy2 + y3
So, the given expression is (3x + y)3 – 9x2y + 3xy2
= (3x + y)3 – 3xy ( 3x – y)
= (3 × 4 – 8)3 – {3 × 4 × -8 (12 + 8)}
= 43 + 12 × 8 × 20 = 64 + 1920 = 1984
Answer choice (d)


Correct Answer: 1984.



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