How do you simplify #12sqrt(-98) - 4sqrt(-50)#?

To simplify (12\sqrt{-98} - 4\sqrt{-50}), you first need to express the square roots in terms of their factors and then simplify them using properties of square roots.

1. Express (\sqrt{-98}) and (\sqrt{-50}) as (\sqrt{-1}) times the square root of a positive number.

2. Simplify each expression separately by factoring out perfect square factors from the radicands.

3. Apply any common factors to simplify further.

So, for (12\sqrt{-98} - 4\sqrt{-50}):

1. ( \sqrt{-98} = \sqrt{-1} \times \sqrt{98} = i \times \sqrt{2 \times 7 \times 7} = 7i\sqrt{2})

2. ( \sqrt{-50} = \sqrt{-1} \times \sqrt{50} = i \times \sqrt{2 \times 5 \times 5} = 5i\sqrt{2})

Now, substitute the simplified forms into the original expression:

(12(7i\sqrt{2}) - 4(5i\sqrt{2}))

This simplifies to:

(84i\sqrt{2} - 20i\sqrt{2})

Finally, combine like terms:

(84i\sqrt{2} - 20i\sqrt{2} = (84 - 20)i\sqrt{2} = 64i\sqrt{2})