CAT Quantitative Aptitude Questions | CAT Algebra - Polynomials questions

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

Video Explanation

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.