(-x%5E2%2B4x%2B6).jpeg "(2x-1)(-x^2+4x+6)")
Expanding the Expression (2x-1)(-x^2+4x+6)
This article will guide you through expanding the expression (2x-1)(-x^2+4x+6). We will use the distributive property (also known as FOIL) to achieve this.
Understanding the Distributive Property (FOIL)
The distributive property states that multiplying a sum by a number is the same as multiplying each addend separately by that number and then adding the products. In the context of binomials, we can use the acronym FOIL to help us remember the order:
- 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 binomials.
Expanding the Expression
Let's apply the FOIL method to our expression:
- First: (2x) * (-x^2) = -2x^3
- Outer: (2x) * (4x) = 8x^2
- Inner: (-1) * (-x^2) = x^2
- Last: (-1) * (4x) = -4x
- Last: (-1) * (6) = -6
Now we combine the terms:
-2x^3 + 8x^2 + x^2 - 4x - 6
Finally, simplify by combining like terms:
-2x^3 + 9x^2 - 4x - 6
Conclusion
Therefore, the expanded form of the expression (2x-1)(-x^2+4x+6) is -2x^3 + 9x^2 - 4x - 6. This process demonstrates the effectiveness of the distributive property in expanding algebraic expressions.