(4-b)(5b^2+5b-4)

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials and Trinomials: (4-b)(5b^2+5b-4)

This article will guide you through the process of multiplying the binomial (4-b) by the trinomial (5b^2+5b-4). This is a fundamental skill in algebra, often encountered when simplifying expressions or solving equations.

Understanding the Process

To multiply these expressions, we'll employ the distributive property. This means we'll multiply each term in the first expression by every term in the second expression.

Step-by-Step Multiplication

1. Distribute the first term of the binomial (4):

   • 4 * 5b^2 = 20b^2
   • 4 * 5b = 20b
   • 4 * -4 = -16

2. Distribute the second term of the binomial (-b):

   • -b * 5b^2 = -5b^3
   • -b * 5b = -5b^2
   • -b * -4 = 4b

3. Combine the results: 20b^2 + 20b - 16 - 5b^3 - 5b^2 + 4b

4. Simplify by combining like terms: -5b^3 + 15b^2 + 24b - 16

The Final Result

Therefore, the product of (4-b) and (5b^2+5b-4) is -5b^3 + 15b^2 + 24b - 16.

Key Takeaways

• Distributive Property: The foundation of multiplying polynomials.
• Combining Like Terms: Crucial for simplifying the final expression.
• Order of Operations: Remember to multiply before combining like terms.