Q. The factor of expression (x + y)³ + (x – y)³ is:
(A) 3x(x² + 3y²)
(B) 2x(x² + 3y²)
(C) 3x(x² – 3y²)
(D) 2x(x² – 3y²)
Question from UPPSC Prelims CSAT 2024
Correct Answer: (B) 2x(x² + 3y²)
Explanation:
To factor the expression (x + y)³ + (x – y)³, let’s expand and simplify it:
(x + y)³ + (x – y)³ = (x³ + 3x²y + 3xy² + y³) + (x³ – 3x²y + 3xy² – y³)
= x³ + 3x²y + 3xy² + y³ + x³ – 3x²y + 3xy² – y³
= 2x³ + 6xy²
= 2x(x² + 3y²)
So, the factored form of (x + y)³ + (x – y)³ is 2x(x² + 3y²).
Answer: Option (B) 2x(x² + 3y²)
