(2x%E2%88%9210)-trinomial.jpeg "(3x−9)(2x−10) Trinomial")
Understanding the Trinomial (3x−9)(2x−10)
The expression (3x−9)(2x−10) is not a trinomial itself, but rather the product of two binomials. A trinomial is a polynomial with three terms. When we multiply the two binomials, we will get a trinomial. Let's break down the process:
Expanding the Expression
We can use the FOIL method (First, Outer, Inner, Last) to expand the product:
- First: (3x)(2x) = 6x²
- Outer: (3x)(-10) = -30x
- Inner: (-9)(2x) = -18x
- Last: (-9)(-10) = 90
Combining the terms, we get: 6x² - 30x - 18x + 90
Finally, we can simplify by combining like terms: 6x² - 48x + 90
Trinomial Result
Therefore, the expanded form of (3x−9)(2x−10) is the trinomial 6x² - 48x + 90.
Further Exploration
We can also analyze this trinomial:
- Leading Coefficient: 6
- Constant Term: 90
- Degree: 2 (highest power of x)
Understanding how to multiply binomials and expand expressions like this is crucial for solving quadratic equations, factoring, and other algebraic manipulations.