(4v%5E2-3v-6).jpeg "(2v+3)(4v^2-3v-6)")
Multiplying Binomials and Trinomials: Expanding (2v+3)(4v^2-3v-6)
This article will guide you through the process of expanding the expression (2v+3)(4v^2-3v-6). This involves multiplying a binomial (two terms) with a trinomial (three terms).
The Distributive Property
The key to expanding this expression is the distributive property. This property states that multiplying a sum by a number is the same as multiplying each term of the sum by the number.
In our case, we can think of (2v+3) as a single term that needs to be distributed across all terms in the trinomial (4v^2-3v-6).
Expanding the Expression
-
Distribute the first term of the binomial (2v) to each term in the trinomial:
- (2v) * (4v^2) = 8v^3
- (2v) * (-3v) = -6v^2
- (2v) * (-6) = -12v
-
Distribute the second term of the binomial (3) to each term in the trinomial:
- (3) * (4v^2) = 12v^2
- (3) * (-3v) = -9v
- (3) * (-6) = -18
-
Combine all the terms you obtained in steps 1 and 2:
- 8v^3 - 6v^2 - 12v + 12v^2 - 9v - 18
-
Simplify the expression by combining like terms:
- 8v^3 + 6v^2 - 21v - 18
The Final Result
Therefore, the expanded form of (2v+3)(4v^2-3v-6) is 8v^3 + 6v^2 - 21v - 18.
Remember, the distributive property is a fundamental concept in algebra. Mastering it is crucial for successfully expanding expressions involving binomials and trinomials.