(7m%5E2-3m-7).jpeg "(m^2-7m-6)(7m^2-3m-7)")
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:
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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
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Distribute the second term of the first trinomial (-7m):
- (-7m)(7m^2) + (-7m)(-3m) + (-7m)(-7) = -49m^3 + 21m^2 + 49m
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Distribute the third term of the first trinomial (-6):
- (-6)(7m^2) + (-6)(-3m) + (-6)(-7) = -42m^2 + 18m + 42
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Combine all the terms:
- 7m^4 - 3m^3 - 7m^2 - 49m^3 + 21m^2 + 49m - 42m^2 + 18m + 42
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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.