(3x%2B4).jpeg "(2x-1)(3x+4)")
Expanding the Expression (2x-1)(3x+4)
This article will explore the process of expanding the expression (2x-1)(3x+4).
Understanding the Concept
The expression (2x-1)(3x+4) represents the multiplication of two binomials. A binomial is a polynomial with two terms. In this case, the two binomials are:
- (2x-1)
- (3x+4)
To expand the expression, we will use the distributive property or the FOIL method.
Expanding using the Distributive Property
The distributive property states that a(b+c) = ab + ac. Applying this property to our expression, we get:
- 2x(3x+4) - 1(3x+4)
Expanding further:
- 6x² + 8x - 3x - 4
Combining like terms:
- 6x² + 5x - 4
Therefore, the expanded form of (2x-1)(3x+4) is 6x² + 5x - 4.
Expanding using the FOIL Method
FOIL stands for First, Outer, Inner, Last, and is a mnemonic device used to remember the order of multiplying terms in a binomial multiplication.
- First: Multiply the first terms of each binomial: 2x * 3x = 6x²
- Outer: Multiply the outer terms: 2x * 4 = 8x
- Inner: Multiply the inner terms: -1 * 3x = -3x
- Last: Multiply the last terms: -1 * 4 = -4
Adding all the terms together:
- 6x² + 8x - 3x - 4
Combining like terms:
- 6x² + 5x - 4
As we can see, the result is the same as using the distributive property.
Conclusion
Expanding the expression (2x-1)(3x+4) results in 6x² + 5x - 4. Both the distributive property and the FOIL method can be used to achieve this outcome. Understanding these methods is crucial for simplifying and manipulating algebraic expressions.