Question

Question 17
Use Structure The product of a monomial and an expression is 4.8x2+1.6xy.
What is the expression if the monomial is 1.6x
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Answer 1

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:

1. For the term \(4.8x^2\):

\[
\frac{4.8x^2}{1.6x} = \frac{4.8}{1.6} \cdot \frac{x^2}{x} = 3x
\]

2. 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:

\[
\boxed{3x + y}
\]