Question
Simplify: (x + y)3 - (x - y)3 - 6y(x2 - y2)
Solution
Let x + y = a, x - y = b
Then, ab = (x + y) (x - y) = x2 - y2
and a - b = (x + y) - (x - y) = 2y
Now, (x + y)3 - (x - y)3 - 6y (x2 - y2)
= (x + y)3 - (x - y)3 - 3(2y) (x2 - y2)
= a3 - b3 - 3(a - b) ab
= (a - b)3 | Using Identity VII
= {(x + y) - (x - y)}3
= (2y)3 = 8y3
