(4x-1)(x^2-7x+1)

Jasonbradley

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Jun 16, 2024

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Expanding the Expression (4x-1)(x^2-7x+1)

This article explores the expansion of the expression (4x-1)(x^2-7x+1).

Understanding the Process

To expand this expression, we will use the distributive property, also known as the FOIL method. FOIL stands for First, Outer, Inner, Last. This method helps us to systematically multiply each term in the first binomial by each term in the second binomial.

Step-by-Step Expansion

1. First: Multiply the first terms of each binomial: 4x * x^2 = 4x^3

2. Outer: Multiply the outer terms of the binomials: 4x * (-7x) = -28x^2

3. Inner: Multiply the inner terms of the binomials: -1 * x^2 = -x^2

4. Last: Multiply the last terms of the binomials: -1 * 1 = -1

Now we have: 4x^3 - 28x^2 - x^2 - 1

Simplifying the Expression

Finally, we combine like terms to get the simplified expression:

4x^3 - 29x^2 - 1

Conclusion

Therefore, the expanded form of (4x-1)(x^2-7x+1) is 4x^3 - 29x^2 - 1.