(2x-9)(3x+4) Trinomial

Jasonbradley

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Jun 16, 2024

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Multiplying Binomials: Expanding (2x-9)(3x+4)

This article will guide you through the process of multiplying the binomials (2x-9) and (3x+4), resulting in a trinomial.

Understanding the Process

The multiplication of binomials is a fundamental concept in algebra. It involves applying the distributive property twice. The distributive property states that multiplying a sum by a number is the same as multiplying each term of the sum by that number.

Expanding the Binomials

1. Multiply the first terms: (2x) * (3x) = 6x²

2. Multiply the outer terms: (2x) * (4) = 8x

3. Multiply the inner terms: (-9) * (3x) = -27x

4. Multiply the last terms: (-9) * (4) = -36

Combining Like Terms

Now we combine the terms we obtained:

6x² + 8x - 27x - 36

Finally, simplify the expression by combining the x terms:

6x² - 19x - 36

The Result

The product of (2x-9) and (3x+4) is the trinomial 6x² - 19x - 36.

Application and Importance

The ability to multiply binomials is essential in various algebraic operations, including:

• Solving quadratic equations
• Factoring trinomials
• Graphing quadratic functions

Understanding this concept is a crucial building block for mastering higher-level algebra.