__Category__: Algebra"Published in Newark, California, USA"

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, x

^{3}is not a perfect square, the factors of x

^{3}are x

^{2}and x. x

^{2}is a perfect square.

At the second term, x

^{2}is a perfect square. The square root of x

^{2}is x.

At the third term, 4y

^{2}is a perfect square. The square root of 4y

^{2}is 2y.

At the fourth term, 8y

^{3}is not a perfect square, the factors of 8y

^{3}are 4y

^{2}and 2y. 4y

^{2}is a perfect square.

Hence, the given equation above becomes

Therefore, the final answer is