(x-2)-as-a-trinomial.jpeg "(3x-5)(x-2) As A Trinomial")
Expanding (3x-5)(x-2) into a Trinomial
This article will guide you through the process of expanding the expression (3x-5)(x-2) into a trinomial.
Understanding the Process
Expanding a product of binomials involves applying the distributive property. In essence, we multiply each term in the first binomial by each term in the second binomial.
Step-by-Step Expansion
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Distribute the first term of the first binomial:
- (3x)(x-2) = 3x² - 6x
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Distribute the second term of the first binomial:
- (-5)(x-2) = -5x + 10
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Combine the results from steps 1 and 2:
- (3x² - 6x) + (-5x + 10) = 3x² - 11x + 10
The Trinomial Result
Therefore, the expanded form of (3x-5)(x-2) as a trinomial is 3x² - 11x + 10.
Key Points
- The resulting trinomial has a leading coefficient of 3, a linear coefficient of -11, and a constant term of 10.
- Expanding binomials is a fundamental skill in algebra and is used in various applications, including solving equations and factoring expressions.