Simplify: (x + y)3 + (x - y)3 + 6x(x2 - y2)

1.	Simplify: (x + y)3 + (x - y)3 + 6x(x2 - y2)
Answer» Let (x + y) = a and (x - y) = b Then, (x + y)³ + (x - y)³ + 6x(x² - y²) = (x + y)³+ (x - y)³+ 3 x 2\(x\) x (x + y)(x - y) = (x + y)³ + (x - y)³- 3 x [(x + y) + (x - y)] x (x + y) + (x - y) = a³ + b³ + 3ab(a + b) = (a + b)³ = (x + y + x - y)³= (2x)³ = 8x³.

Answer»

Let (x + y) = a and (x - y) = b

Then, (x + y)³ + (x - y)³ + 6x(x² - y²) = (x + y)³+ (x - y)³+ 3 x 2\(x\) x (x + y)(x - y)

= (x + y)³ + (x - y)³- 3 x [(x + y) + (x - y)] x (x + y) + (x - y)

= a³ + b³ + 3ab(a + b)

= (a + b)³ = (x + y + x - y)³= (2x)³ = 8x³.

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