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Perform the indicated operations
Solution:
Consider the given equation above
If you will cube a radical in which the index is 2 or that have a square root sign, then the terms inside the square root sign will be raised to a third power.
If you will multiply a radical with another radical with the same index, then the terms inside the radicals will be multiplied together. In this case, the given above equation can be written as follows
Apply the principles of Binomial Theorem or squaring of a binomial to the above equation as follows
At the first term, x3 is not a perfect square, the factors of x3 are x2 and x. x2 is a perfect square.
At the second term, x2 is a perfect square. The square root of x2 is x.
At the third term, 4y2 is a perfect square. The square root of 4y2 is 2y.
At the fourth term, 8y3 is not a perfect square, the factors of 8y3 are 4y2 and 2y. 4y2 is a perfect square.
Hence, the given equation above becomes
Therefore, the final answer is
