Expanding and Simplifying the Expression (m^2  7m  6)(7m^2  3m  7)
This article will walk you through the process of expanding and simplifying the given expression: (m^2  7m  6)(7m^2  3m  7)
Understanding the Problem:
We have two trinomials being multiplied together. To simplify this, we need to perform the multiplication using the distributive property (also known as FOIL for binomials).
Steps to Simplify:

Distribute the first term of the first trinomial (m^2):
 (m^2)(7m^2) + (m^2)(3m) + (m^2)(7) = 7m^4  3m^3  7m^2

Distribute the second term of the first trinomial (7m):
 (7m)(7m^2) + (7m)(3m) + (7m)(7) = 49m^3 + 21m^2 + 49m

Distribute the third term of the first trinomial (6):
 (6)(7m^2) + (6)(3m) + (6)(7) = 42m^2 + 18m + 42

Combine all the terms:
 7m^4  3m^3  7m^2  49m^3 + 21m^2 + 49m  42m^2 + 18m + 42

Combine like terms:
 7m^4  52m^3  28m^2 + 67m + 42
Simplified Expression:
The simplified form of the expression (m^2  7m  6)(7m^2  3m  7) is 7m^4  52m^3  28m^2 + 67m + 42.
Key Points:
 The distributive property is crucial for expanding expressions like this.
 Combining like terms helps to simplify the expression to its final form.
Note: This is a relatively complex expression, and the simplification process can be challenging. Practice and understanding the distributive property are essential for success.