(4x%5E2-2x-3).jpeg "(3x-5)(4x^2-2x-3)")
Expanding the Expression (3x-5)(4x^2-2x-3)
This article will explore how to expand the expression (3x-5)(4x^2-2x-3). This involves applying the distributive property (often referred to as FOIL) to multiply the two binomials.
The Distributive Property (FOIL)
The distributive property states that to multiply two binomials, each term in the first binomial must be multiplied by each term in the second binomial. This can be remembered by the acronym FOIL:
- First: Multiply the first terms of each binomial.
- Outer: Multiply the outer terms of each binomial.
- Inner: Multiply the inner terms of each binomial.
- Last: Multiply the last terms of each binomial.
Expanding the Expression
Let's apply FOIL to our expression:
- First: (3x) * (4x^2) = 12x^3
- Outer: (3x) * (-2x) = -6x^2
- Inner: (-5) * (4x^2) = -20x^2
- Last: (-5) * (-2x) = 10x
- Last: (-5) * (-3) = 15
Now we combine the like terms:
12x^3 - 6x^2 - 20x^2 + 10x + 15 = 12x^3 - 26x^2 + 10x + 15
Conclusion
Therefore, the expanded form of (3x-5)(4x^2-2x-3) is 12x^3 - 26x^2 + 10x + 15. This process of expanding binomials is crucial in algebra and other areas of mathematics where you need to manipulate and simplify expressions.