Question

Add.

In this problem, x > 0.
3√4x5 - 32x5

A 12V/4x5
B 8x√4x²
C 5x√4x²
D 10x³4x²

Answer 1

The expression
`\(3√(4x^5) - 3√(2x^5)\)` simplifies to
`\(3x^{(5)/(2)}(2 - √(2))\)`. None of the provided options (A, B, C, D) matches the simplified expression.

To simplify the expression
`\(3√(4x^5) - 3√(2x^5)\)`, let's break down each term separately.

1. First term:
`\(3√(4x^5)\)`:

-
`\(3 * √(4x^5)\)` can be simplified as
`\(3 * 2x^{(5)/(2)}\) since \(√(4x^5) = 2x^{(5)/(2)}\).`

- So, the first term becomes
`\(6x^{(5)/(2)}\).`

2. Second term:
`\(3√(2x^5)\)`:

-
`\(3 * √(2x^5)\)` can be simplified as
`\(3 * √(2) * x^{(5)/(2)}\)`.

- The second term remains
`\(3√(2)x^{(5)/(2)}\)`.

Now, subtract the second term from the first:

`\[ 6x^{(5)/(2)} - 3√(2)x^{(5)/(2)} \]`

Factor out the common term
`\(3x^{(5)/(2)}\)`:

`\[ 3x^{(5)/(2)}(2 - √(2)) \]`

Therefore, the simplified expression is
`\(3x^{(5)/(2)}(2 - √(2))\)`.

None of the provided options (A, B, C, D) matches the simplified expression.