Simplify  12xy25xz·15xz2y2.12𝑥𝑦25𝑥𝑧·15𝑥𝑧2𝑦2. Multiple choice question.A)36xzy236𝑥𝑧𝑦2 B)3xz23𝑥𝑧2 C)36xz36𝑥𝑧 D)3x2zy2

1. Break Down the Problem

To simplify the expression $12xy25xz \cdot 15xz^2y^2$, we will first multiply the coefficients and then combine the variables.

2. Relevant Concepts

We will use the following concepts:

• Multiplication of coefficients.
• Properties of exponents to combine like bases.
• The distributive property.

3. Analysis and Detail

1. Multiply the coefficients: $12 \times 15 = 180$

2. Combine the variables:

   • For $xy$ from the first term and $y^2$ from the second term: $y \times y^2 = y^{1 + 2} = y^3$
   • For $xz$ from the first term and $xz^2$ from the second term: $x \times x = x^{1 + 0} = x^1 \quad \text{and} \quad z \times z^2 = z^{1 + 2} = z^3$

Combining all parts together we have: $180 \cdot x \cdot z^3 \cdot y^3$

4. Verify and Summarize

Now we need to check which option matches our simplified expression. Since the expression is: $180xyz^3y^3$

Next, we can simplify $180$ to see if this appears in the options.

*We can factor $180 = 36 \times 5$ to simplify to: $36xyz^3y^3$

This is not a match, but for many responses, we could simplify 36xyz^2 also, checking all values resulted in: $36xy^3z^3$

This does not match.

Final Answer

Since there seems to be some confusion in options, but based on standard simplification from calculations we can rationally summarize our answer; None of the options precisely reflect the result, the closest would be: $36xyz^2$ based on individual variable standardization format from original values.