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Simplify (x+y)^3 - (x-y)^3 - 6y …

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Simplify (x+y)^3 - (x-y)^3 - 6y (x+y) (x-y)

Posted by Smita Tripathi 5 years, 5 months ago

CBSE > Class 09 > Mathematics

1 answers

Gaurav Seth 5 years, 5 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

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