CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

CAT Questions | Algebra | Polynomials - Cubic Equation

The question is about Cubic Equation. Some algebraic simplification before substituting would make the process simple. Think in terms Algebraic expansion. Polynomials is a simple topic which involves a lot of basic ideas. Make sure that you a get of hold of them by solving these questions. A range of CAT questions can be asked based on this simple concept.

Question 10: What is the value of 27x3 + 18x2y + 12xy2 + y3 when x = 4, y = – 8?

  1. 64
  2. 256
  3. 512
  4. 1984

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Explanatory Answer

Method of solving this CAT Question from CAT Algebra - Polynomials: Direct substitution is a lengthy process!

(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

The question is "What is the value of 27x3 + 18x2y + 12xy2 + y3 when x = 4, y = – 8? "

Hence the answer is "1984"

Choice D is the correct answer.

 


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