(x%2B5)-as-a-trinomial.jpeg "(2x-3)(x+5) As A Trinomial")
Expanding (2x-3)(x+5) into a Trinomial
In this article, we'll explore how to expand the expression (2x-3)(x+5) into a trinomial.
Understanding the Concept
A trinomial is a polynomial with three terms. To expand the given expression, we'll use the distributive property (also known as the FOIL method).
Applying the FOIL Method
The FOIL method stands for:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of the binomials.
- Inner: Multiply the inner terms of the binomials.
- Last: Multiply the last terms of each binomial.
Let's apply this to our expression:
F: (2x)(x) = 2x² O: (2x)(5) = 10x I: (-3)(x) = -3x L: (-3)(5) = -15
Combining Like Terms
Now we have: 2x² + 10x - 3x - 15
Combining the like terms (10x and -3x) gives us:
2x² + 7x - 15
Final Result
Therefore, the expanded form of (2x-3)(x+5) as a trinomial is 2x² + 7x - 15.