Decompose the Expression: 15xyz² + 25xy/z Step by Step

Which of the expressions is a decomposition of the simplified expression below?

$15xyz^2+25\frac{xy}{z}$

To solve the problem, we aim to factor the expression by identifying the greatest common factor (GCF) for the terms $15xyz^2$ and $25\frac{xy}{z}$.

Step 1: Identify the GCF
- Both terms contain the factors $x$ and $y$.
- The first term $15xyz^2$ consists of $15$, $x$, $y$, and $z^2$.
- The second term $25\frac{xy}{z}$ consists of $25$, $x$, $y$, and $\frac{1}{z}$.
- The GCF of the constants 15 and 25 is 5.

Step 2: Factor out the GCF
- The GCF of the variables is $xy$.
- Therefore, the overall GCF we can factor out is $5xy$.

Step 3: Simplify the remaining expression
- Factoring out $5xy$ from the expression:
$15xyz^2 = 5xy \times 3z^2$
$25\frac{xy}{z} = 5xy \times \frac{5}{z}$

Step 4: Write the factored expression
This gives us:
$15xyz^2 + 25\frac{xy}{z} = 5xy(3z^2 + \frac{5}{z})$

Thus, the decomposition of the simplified expression is $5xy(3z^2 + \frac{5}{z})$, which corresponds to choice 2.

Therefore, the solution to the problem is $5xy(3z^2 + \frac{5}{z})$.