(2x%5E2-5x-3).jpeg "(2x-1)(2x^2-5x-3)")
Expanding the Expression (2x-1)(2x^2-5x-3)
This article explores the process of expanding the expression (2x-1)(2x^2-5x-3). We'll use the distributive property to multiply each term in the first factor by each term in the second factor.
Step 1: Distributing the First Term
First, distribute the 2x from the first factor to each term in the second factor:
2x * (2x^2 - 5x - 3) = 4x^3 - 10x^2 - 6x
Step 2: Distributing the Second Term
Next, distribute the -1 from the first factor to each term in the second factor:
-1 * (2x^2 - 5x - 3) = -2x^2 + 5x + 3
Step 3: Combining Like Terms
Finally, combine the like terms from both results:
4x^3 - 10x^2 - 6x - 2x^2 + 5x + 3
= 4x^3 - 12x^2 - x + 3
Conclusion
Therefore, the expanded form of the expression (2x-1)(2x^2-5x-3) is 4x^3 - 12x^2 - x + 3. This process showcases the power of the distributive property in simplifying expressions.