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Question
What should be added to x3 + 3x2y + 3xy2 + y3 to get x3 + y3?
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Solution
In order to find the solution subtract x3 + 3x2y + 3xy2 + y3 from x3 + y3
Required expression is x3 + y3 – (x3 + 3x2y + 3xy2 + y3) = x3 + y3 – x3 – 3x2y – 3xy2 – y3
On combining the like terms,
= x3 – x3 + y3 – y3 – 3x2y – 3xy2
= –3x2y – 3xy2
So, if we add –3x2y – 3xy2 in x3 + 3x2y + 3xy2 + y3, we get x3 + y3.
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