(x^2+5x-1)(5x^2-6x+1)

Jasonbradley

2 min read

·

Jun 17, 2024

21

Share

Expanding the Expression (x^2 + 5x - 1)(5x^2 - 6x + 1)

This article will guide you through the process of expanding the given expression: (x^2 + 5x - 1)(5x^2 - 6x + 1). We will achieve this by utilizing the distributive property of multiplication.

Expanding the Expression

The distributive property states that for any numbers a, b, and c:

• a(b + c) = ab + ac

To expand our expression, we'll treat each term in the first set of parentheses as a separate multiplier and multiply it by each term in the second set of parentheses.

1. Multiply x^2 by each term in the second set of parentheses:

   • x^2 * (5x^2 - 6x + 1) = 5x^4 - 6x^3 + x^2

2. Multiply 5x by each term in the second set of parentheses:

   • 5x * (5x^2 - 6x + 1) = 25x^3 - 30x^2 + 5x

3. Multiply -1 by each term in the second set of parentheses:

   • -1 * (5x^2 - 6x + 1) = -5x^2 + 6x - 1

4. Combine all the resulting terms:

   • 5x^4 - 6x^3 + x^2 + 25x^3 - 30x^2 + 5x - 5x^2 + 6x - 1

5. Simplify by combining like terms:

   • 5x^4 + 19x^3 - 34x^2 + 11x - 1

Conclusion

Therefore, the expanded form of (x^2 + 5x - 1)(5x^2 - 6x + 1) is 5x^4 + 19x^3 - 34x^2 + 11x - 1. This method of expanding expressions is crucial for understanding and manipulating polynomial functions in various mathematical contexts.