Understanding the Value of MN Given M and N

In this article, we will help you solve a math problem that often comes up in discussions about SEO optimization and keyword analysis. This involves understanding the relationship between M and N, given the following expressions:

Mx-y-z

Nxyz

We need to find the value of MN. Let's break it down step by step:

Step 1: Determine the Expression for MN

Given:

MN (x-y-z) * xyz

This can be simplified as follows:

MN x * xyz - y * xyz - z * xyz

Further simplification yields:

MN x2yz - xyz2 - xy2z

However, the problem states that:

MN 2x

This implies that the terms involving y and z cancel each other out. This is a critical point for understanding the problem effectively.

Step 2: Canceling Out Terms Involving y and z

Let's analyze the terms more closely. We know that:

MN x 2yz - xyz2 - xy2z

For the expression to be equal to 2x, the terms involving y and z must cancel each other out. This is only possible if the signs and the coefficients of these terms result in a net cancellation.

Step 3: Solving for the Given Expression

Given:

MN (x-y-z)xyz

And we are told:

MN 2x

This implies that the expression simplifies to:

MN x2yz - xyz2 - xy2z 2x

Hence, the terms involving y and z cancel out, leading to:

MN 2x

Conclusion

The value of MN given the expressions Mx-y-z and Nxyz simplifies to 2x. This solution is significant for understanding the relationship between variables and coefficients in algebraic expressions, which has broader applications in SEO, keyword analysis, and other mathematical problem-solving contexts.