the expression 4ab(square root of)2b-3a(square root of)18b^3+7ab(square root of)6b is equivalent to...

(a)2ab(square root of)6b
(b)16ab(square root of)2b
(c)-5ab+7ab(square root of)6b
(d)-5ab(square root of)2b+7ab(square root of)6b
Please help its due monday!

4ab√(2b) - 3a√(18b^3) + 7ab√(6b)

= 4ab√(2b) - 3a(3b)√(2b) + 7ab√(6b)
= -5ab√(2b) + 7ab√(6)

Thank you once again

To simplify the expression 4ab√2b - 3a√18b^3 + 7ab√6b, let's break it down step-by-step:

Step 1: Simplify the square roots individually:
- The square root of 2 can't be simplified further, so it remains as √2.
- The square root of 18 can be simplified as √(9 × 2) = √9 × √2 = 3√2.
- The square root of b^3 can be simplified as √(b^2 × b) = b√b.
- The square root of 6 can't be simplified further, so it remains as √6.

Step 2: Combine like terms:
Here, we have three terms: 4ab√2b, -3a√18b^3, and 7ab√6b.

- For the first term, we have √2, so that remains unchanged: 4ab√2b.
- For the second term, we have √18 = 3√2 and √b^3 = b√b: -3a(3√2b√b) = -9ab√2b^2 = -9ab√2b^2.
- For the third term, we have √6, so it remains unchanged: 7ab√6b.

The simplified expression is now: 4ab√2b - 9ab√2b^2 + 7ab√6b.

Step 3: Combine like terms again:
We see that the first and last term have the same square roots, so we can combine them: 4ab√2b + 7ab√6b = 11ab√2b + 7ab√6b.

The simplified expression is now: 11ab√2b + 7ab√6b - 9ab√2b^2.

Now, let's look at the answer choices:
(a) 2ab√6b
(b) 16ab√2b
(c) -5ab + 7ab√6b
(d) -5ab√2b + 7ab√6b

By comparing the simplified expression to the answer choices, we can see that the correct answer is (d) -5ab√2b + 7ab√6b.

So, the expression 4ab√2b - 3a√18b^3 + 7ab√6b is equivalent to -5ab√2b + 7ab√6b.

To simplify the given expression, let's break it down into smaller parts and combine like terms.

Given expression: 4ab√(2b) - 3a√(18b^3) + 7ab√(6b)

First, let's simplify each term using the properties of square roots:

Term 1: 4ab√(2b) = 4ab√2 * √b

Term 2: - 3a√(18b^3) = -3a√(9 * 2 * b^2 * b) = -3a * 3b * √(2b) = -9ab√(2b^3)

Term 3: 7ab√(6b) - This term is already simplified.

Now, let's combine like terms:

Final expression: (4ab√2 * √b) - (9ab√(2b^3)) + (7ab√(6b))

To combine like terms, we need to have the same base inside the square root:

Term 1: 4ab√2 * √b = 4ab√(2b^2) = 4ab(b)√2 = 4ab^2√2

Term 2: -9ab√(2b^3) = -9ab(b√2) = -9ab^2√2

Now, let's rewrite the expression with the simplified terms:

Final expression: (4ab^2√2) - (9ab^2√2) + (7ab√(6b))

Next, let's combine the like terms with the same coefficients (√2):

(4ab^2√2) - (9ab^2√2) = (4ab^2 - 9ab^2)√2 = (-5ab^2)√2

Now, let's rewrite the final expression:

Final expression: (-5ab^2)√2 + (7ab√(6b))

So, the equivalent expression is -5ab^2√2 + 7ab√(6b).

Therefore, the answer is (d) -5ab√2b + 7ab√(6b).