(x-2)-as-a-trinomial.jpeg "(2x+10)(x-2) As A Trinomial")
Expanding (2x + 10)(x - 2) into a Trinomial
This article will guide you through the process of expanding the product of two binomials, (2x + 10)(x - 2), resulting in a trinomial.
Understanding Binomials and Trinomials
- Binomials: These are algebraic expressions consisting of two terms, typically separated by a plus or minus sign. Examples: (2x + 10), (x - 2)
- Trinomials: These are algebraic expressions consisting of three terms, typically separated by plus or minus signs. Example: ax² + bx + c
Expanding using the FOIL Method
The FOIL method is a mnemonic device to help remember the steps for multiplying two binomials:
- 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 FOIL to (2x + 10)(x - 2):
- First: (2x)(x) = 2x²
- Outer: (2x)(-2) = -4x
- Inner: (10)(x) = 10x
- Last: (10)(-2) = -20
Now, we combine the terms: 2x² - 4x + 10x - 20
Finally, simplify by combining like terms: 2x² + 6x - 20
The Result
Therefore, the expanded form of (2x + 10)(x - 2) as a trinomial is 2x² + 6x - 20.