Simplify the radicals and collect the like terms
√180m^4 - m^2√125 +2m√147m - √75m^3
To simplify the radicals, we can rewrite the numbers inside the square roots as the product of their perfect square factors.
√180m^4 can be simplified as √(36 * 5 * m^4) = 6m^2√5
√125 can be simplified as √(25 * 5) = 5√5
2m√147m can be simplified as 2m√(49 * 3m) = 14m√(3m)
√75m^3 can be simplified as √(25 * 3 * m^3) = 5m√(3m)
Now we can collect like terms by combining the simplified radicals:
6m^2√5 - m^2√5 + 14m√(3m) - 5m√(3m)
Combining like terms, we get:
(6m^2 - m^2)√5 + (14m - 5m)√(3m)
Simplifying further:
5m^2√5 + 9m√(3m)