(7v-2).jpeg "(2v-1)(7v-2)")
Expanding the Expression (2v-1)(7v-2)
This article will guide you through the process of expanding the expression (2v-1)(7v-2). This involves applying the distributive property, often referred to as FOIL.
Understanding FOIL
FOIL is a mnemonic acronym that 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.
Expanding the Expression
Let's apply FOIL to our expression:
- First: (2v) * (7v) = 14v²
- Outer: (2v) * (-2) = -4v
- Inner: (-1) * (7v) = -7v
- Last: (-1) * (-2) = 2
Now, we combine the terms:
14v² - 4v - 7v + 2
Finally, simplify by combining like terms:
14v² - 11v + 2
Conclusion
Therefore, the expanded form of the expression (2v-1)(7v-2) is 14v² - 11v + 2. Remember, applying the FOIL method allows us to efficiently expand expressions involving binomials.