(x + y)3 - (x - y)3 can be factorized as: - Vidyadip

MCQ

(x + y)³ - (x - y)³ can be factorized as:

A
2x(3x² + y²)
B
2y(3y² + x²)
C
2y(3x² + y²)
D
2x(x² + 3y²)

✓

Answer

2y(3x² + y²)
Solution:
Put a = x + y and b = x - y, then
(x + y)³ - (x - y)³ = a³ - b³= (a − b) (a² + b² + ab)
= (x + y - x + y) [(x + y)² + (x - y)² + (x - y) (x+y)]
=2y[2(x² + y²) + (x² - y²)]
=2y[3x² + y²]

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