(3x%2B5)-as-a-trinomial.jpeg "(2x-3)(3x+5) As A Trinomial")
Expanding (2x-3)(3x+5) into a Trinomial
This article will guide you through the process of expanding the expression (2x-3)(3x+5) and writing it as a trinomial.
Understanding Trinomials
A trinomial is a polynomial with three terms. Each term is a product of a coefficient and one or more variables raised to non-negative integer powers.
Expanding the Expression
To expand (2x-3)(3x+5), we can use the distributive property (also known as FOIL method):
- First: Multiply the first terms of each binomial: (2x)(3x) = 6x²
- Outer: Multiply the outer terms: (2x)(5) = 10x
- Inner: Multiply the inner terms: (-3)(3x) = -9x
- Last: Multiply the last terms: (-3)(5) = -15
Now, combine the terms:
6x² + 10x - 9x - 15
Simplify by combining like terms:
6x² + x - 15
The Trinomial Form
The expanded form of (2x-3)(3x+5) is 6x² + x - 15, which is a trinomial.
Summary
By using the distributive property, we successfully expanded the expression (2x-3)(3x+5) into the trinomial 6x² + x - 15. This process demonstrates a fundamental operation in algebra, and it's crucial for understanding and manipulating polynomial expressions.