Question

Which choice is equivalent to the expression below?
5x√2-3√2+x√2

Answer 1

You did not list any choices but if you simplify that the answer is 6√2x-3√2

Explanation:

If they want you to factor it instead of simplifying the answer is 3√2(2x-1)

Answer 2

`6x√(2) - 3√(2)`

Explanation:

So you haven't provided any options, but I'm assuming they want it in most simplified form.

To do this, we simply combine like terms, and in this case you can see the
`√(2)` as a variable, if it makes it easier to think about why we can combine terms. So just like how we can do:
`2y + y = 3y` we can do the same thing here, since sqrt(2) constant and it's in each expression.

So if it makes a bit easier to represent, I'll rewrite the equation such that sqrt(2) = y

`5xy-3y+xy`

So in here, think of y as the variable and the 5x, -3, and x as the coefficients.

In doing this we can combine the terms by adding them, since they all have the same "variable" (sqrt(2))

`(5x-3+x)y`

Simplify this expression to get

`(6x-3)y`

Now just plug the sqrt(2) back in as y and you get the expression

`(6x-3)√(2)`

Since we can't combine the 6x and -3 in any way, we we can just distribute this back into the sqrt(2)

`6x√(2) - 3√(2)`