SOLUTION: multiplication problem: (2 sqrt. 5xy) (2 sqrt. 10x^2y^3) thank you for your help!!

Question 188724: multiplication problem:
(2 sqrt. 5xy) (2 sqrt. 10x^2y^3)
thank you for your help!!
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
Start with the given expression.

Rearrange the terms.

Multiply 2 and 2 to get 4

Combine the roots using the identity

Rearrange the terms inside the root.

Multiply 5 and 10 to get 50

Multiply the variable terms by adding the exponents.

Add

Factor into

Factor into

Factor into

Break up the square root using the identity .

Take the square root of to get .

Multiply 4 and 5 to get 20

Take the square root of to get .

Take the square root of to get .

Rearrange and multiply the terms.

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Answer:

So simplifies to

In other words, where every variable is non-negative.

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