1. **State the problem:** Find the value of the expression $$4a^{2} - ab$$ for $$a = 1.47$$ and $$b = 5.78$$. 2. **Write the formula:** The expression is $$4a^{2} - ab$$. 3. **Substitute the values:** Replace $$a$$ and $$b$$ with the given numbers: $$4(1.47)^{2} - (1.47)(5.78)$$ 4. **Calculate each term:** Calculate $$a^{2}$$: $$1.47^{2} = 2.1609$$ Multiply by 4: $$4 \times 2.1609 = 8.6436$$ Calculate $$ab$$: $$1.47 \times 5.78 = 8.4966$$ 5. **Substitute back and simplify:** $$8.6436 - 8.4966 = 0.147$$ 6. **Final answer:** $$\boxed{0.147}$$