Simplify (x+y)^3 - (x-y)^3 - 6y …
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Gaurav Seth 4 years, 3 months ago
Given, (x+y)3 - (x-y)3 - 6y (x+y) (x-y)
Answer : 8y3
Explanation:
(x+y)3 - (x-y)3 - 6y (x+y) (x-y)
= (x + y)3 - (x - y)3 - 6y(x2 - y2)
Now, 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
0Thank You