(x+y)³-(x-y)³ can be factorized as:
A. 2y(3x² +y² )
B. 2x(3x² +y² )
C. 2y(3y² +x² )
D. 2x(x² +3y² )
Answers
Given: (x + y)³ - (x - y)³
In order to factorise the given algebraic expression we use the following Identity - (a + b)³ = a³ + b³ + 3a²b + 3ab² & (a - b)³ = a³ - b³ - 3a²b + 3ab² :
= x³ + y³ + 3x²y + 3xy² - (x³ - y³ - 3x²y + 3xy²)
= x³ + y³ + 3x²y + 3xy² - x³ + y³ + 3x²y - 3xy²
= x³ - x³ + y³ + y³ + 3x²y + 3x²y + 3xy² - 3xy²
= 2y³ + 6x²y
Taking 2y common :
= 2y(y² + 3x²)
Hence, (x + y)³ - (x - y)³ can be factorized as 2y(y² + 3x²).
Option (A) 2y(y² + 3x²) is correct.
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