(1−4m)(m2−3m+8)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (1−4m)(m2−3m+8)

This article will explore how to expand the expression (1−4m)(m2−3m+8) using the distributive property.

Understanding the Distributive Property

The distributive property states that multiplying a sum by a number is the same as multiplying each addend by the number and then adding the products. Mathematically, this can be expressed as:

a(b + c) = ab + ac

Expanding the Expression

To expand the expression (1−4m)(m2−3m+8), we can use the distributive property twice:

1. Distribute (1−4m) over the terms in the second set of parentheses:

   (1−4m)(m2−3m+8) = (1)(m2−3m+8) + (-4m)(m2−3m+8)

2. Distribute the constants 1 and -4m over the terms within the parentheses:

   (1)(m2−3m+8) + (-4m)(m2−3m+8) = (m2 - 3m + 8) + (-4m3 + 12m2 - 32m)

3. Combine like terms:

   (m2 - 3m + 8) + (-4m3 + 12m2 - 32m) = -4m3 + 13m2 - 35m + 8

Conclusion

Therefore, the expanded form of the expression (1−4m)(m2−3m+8) is -4m3 + 13m2 - 35m + 8. This process demonstrates how the distributive property is crucial for expanding and simplifying expressions involving multiple terms.