4x-(5x-1)(x%2B3).jpeg "(2x-3)4x-(5x-1)(x+3)")
Expanding and Simplifying the Expression (2x-3)4x-(5x-1)(x+3)
This article explores the process of expanding and simplifying the given algebraic expression: (2x-3)4x-(5x-1)(x+3).
Expanding the Expression
We begin by applying the distributive property to both parts of the expression:
-
(2x-3)4x: Multiplying each term within the parentheses by 4x, we get:
- 2x * 4x = 8x²
- -3 * 4x = -12x
- (2x-3)4x = 8x² - 12x
-
(5x-1)(x+3): We expand this product using the FOIL method (First, Outer, Inner, Last):
- 5x * x = 5x²
- 5x * 3 = 15x
- -1 * x = -x
- -1 * 3 = -3
- (5x-1)(x+3) = 5x² + 14x - 3
Combining the Expanded Terms
Now, we have the following: (2x-3)4x-(5x-1)(x+3) = 8x² - 12x - (5x² + 14x - 3)
Finally, we simplify by distributing the negative sign and combining like terms:
- 8x² - 12x - 5x² - 14x + 3
- (8x² - 5x²) + (-12x - 14x) + 3
- 3x² - 26x + 3
Conclusion
By expanding and simplifying the expression (2x-3)4x-(5x-1)(x+3), we arrive at the simplified form 3x² - 26x + 3. This process demonstrates the importance of applying distributive property and combining like terms for algebraic simplification.