# Multiplying Variables: How to Multiply (3√2x)(3√2x) | Homework Help

• Stratosphere
In summary, the student attempted to solve a problem asking how to multiply something like (2-\sqrt{x-1})(2-\sqrt{x-1}), but was unable to figure out the correct steps. After doing some research, they found that commutative and associative properties would let them group the like factors together.
Stratosphere

## Homework Statement

How would I multiply this together? (3$$\sqrt{2x}$$)(3$$\sqrt{2x}$$)

## The Attempt at a Solution

I can't seem to be able to figure out how to multiply them, i keep getting an answer that is too short.

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What do you get?? And are those supposed to be cube roots or 3 times a square root?

3 times a square root. Sorry if it’s not clear.

That's fine. So what did you get?

Well you should be able to say what $\sqrt{2x}\sqrt{2x}$ is just from the definition of square root! And I'm sure you know what (3)(3) is!

But are you absolutely sure it is $(3\sqrt{2x})(3\sqrt{2x})$? That's seems a peculiar way to write a very simple question. $(\sqrt[3]{2x})(\sqrt[3]{2x})$ is a much more reasonable (and slightly harder) question.

Let me rephrase the question. I want to know how to multiply somthing like
(2-$$\sqrt{x-1}$$)(2-$$\sqrt{x-1}$$), in other words, how to square a side that has variables in a radical.
After i did this out i got
-4$$\sqrt{x-1}$$+x+3

Stratosphere said:
Let me rephrase the question. I want to know how to multiply somthing like
(2-$$\sqrt{x-1}$$)(2-$$\sqrt{x-1}$$), in other words, how to square a side that has variables in a radical.
After i did this out i got
-4$$\sqrt{x-1}$$+x+3

And what could be wrong with that?

Commutative and associative properties will let you group the like factors together. You see each factor is squared. 3$$\bullet$$3$$\bullet$$$$\sqrt{2x}$$$$\sqrt{2x}$$, and then just one or two more steps if any.

EDIT: While trying to edit this, to fix the LARGE dots representing multiplication, the typesetting formatting tool is gone; those should really be small dots as can be common for showing multiplication operation. I do not have many of these tags memorized for TEX.

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Let me continue:

(3)(3)$$\sqrt{2}$$$$\sqrt{2}$$$$\sqrt{x}$$$$\sqrt{x}$$

edit: this time, the forum will NOT permit me to put in the missing square root of x. It is present in the message edit field, but will not appear in the resulting forum message.

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## 1. What are variables?

Variables are symbols or letters that represent unknown or changing values in mathematical equations.

## 2. How do you multiply variables?

To multiply variables, you simply multiply the coefficients (numbers in front of the variables) and then multiply the variables using the exponent rules. For example, 2x * 3x = 6x2.

## 3. Can you multiply variables with different exponents?

Yes, you can multiply variables with different exponents. Just remember to use the exponent rules and add the exponents when multiplying variables with the same base. For example, x2 * x3 = x5.

## 4. Can you multiply variables with different bases?

No, you cannot multiply variables with different bases. In order to multiply variables, they must have the same base. If the bases are different, you can simplify the expression by factoring out the common variables and coefficients.

## 5. Can you multiply variables with different types, such as letters and numbers?

Yes, you can multiply variables with different types, as long as they follow the rules of multiplication. For example, 3x * y = 3xy. However, it is important to note the difference between variables and constants. Variables represent changing values, while constants represent fixed values.

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