To find the expression that, when multiplied by the monomial \(1.6x\), gives the result \(4.8x^2 + 1.6xy\), we can set up the equation:
\[ 1.6x \cdot \text{Expression} = 4.8x^2 + 1.6xy \]
To isolate the expression, we can divide both sides of the equation by \(1.6x\):
\[ \text{Expression} = \frac{4.8x^2 + 1.6xy}{1.6x} \]
Now we can simplify the right side. We can separate the terms in the numerator:
- For the term \(4.8x^2\):
\[ \frac{4.8x^2}{1.6x} = \frac{4.8}{1.6} \cdot \frac{x^2}{x} = 3x \]
- For the term \(1.6xy\):
\[ \frac{1.6xy}{1.6x} = \frac{1.6}{1.6} \cdot \frac{xy}{x} = y \]
Now, we can combine these results:
\[ \text{Expression} = 3x + y \]
Thus, the expression that when multiplied by the monomial \(1.6x\) gives \(4.8x^2 + 1.6xy\) is:
\[ \boxed{3x + y} \]