Final answer:
To find the product of the given expression, simplify the expression inside the square root, multiply it by the expression outside the square root, and then square the entire expression. The final product is 112x⁶.
Step-by-step explanation:
To find the product of the expression (4x√5x²+2x²6)², we need to simplify it first. Start by simplifying the expression inside the square root, which is 5x²+2x²6. Combine like terms to get 7x²6.
Next, simplify the expression outside the square root, which is 4x√7x²6. Multiply 4x by the square root of 7x²6 to get 4x√7x²6.
Finally, square the entire expression 4x√7x²6 to get (4x√7x²6)² = (4x√7x²6)(4x√7x²6) = 16x²(7x²6) = 16x⁴7x²6 = 112x⁶. Therefore, the product of (4x√5x²+2x²6)² is 112x⁶.