Question:

Compare Quantity A and Quantity B: \[ \text{Quantity A: } (x + y)^3, \quad \text{Quantity B: } x^3 + y^3 \] Given that \( x<0 \) and \( y>0 \), compare the two quantities.

Show Hint

When comparing expressions with variables, always consider the sign and magnitude of each term.
Updated On: Sep 30, 2025
  • The relationship cannot be determined.
  • The two quantities are equal.
  • Quantity B is greater.
  • Quantity A is greater.
Hide Solution
collegedunia
Verified By Collegedunia

The Correct Option is A

Solution and Explanation

Step 1: Examine the expressions.
We are given \( (x + y)^3 \) and \( x^3 + y^3 \). The expression \( (x + y)^3 \) expands as: \[ (x + y)^3 = x^3 + 3x^2y + 3xy^2 + y^3. \]
Step 2: Analyze the given conditions.
Since \( x<0 \) and \( y>0 \), the term \( 3x^2y + 3xy^2 \) may be positive or negative depending on the values of \( x \) and \( y \), and therefore the comparison cannot be determined definitively.
Step 3: Conclusion.
Thus, the relationship between the two quantities cannot be determined without more information.
Was this answer helpful?
0
0

Questions Asked in GRE exam

View More Questions