(x%5E2-3x-7).jpeg "(2x-1)(x^2-3x-7)")
Expanding the Expression (2x - 1)(x² - 3x - 7)
This article will guide you through expanding the expression (2x - 1)(x² - 3x - 7) using the distributive property (also known as FOIL method).
Understanding the Distributive Property
The distributive property states that multiplying a sum by a number is the same as multiplying each addend of the sum by the number and then adding the products.
In our case, we need to distribute each term in the first binomial (2x - 1) to each term in the second binomial (x² - 3x - 7).
Expanding the Expression
-
Multiply 2x by each term in the second binomial:
- 2x * x² = 2x³
- 2x * -3x = -6x²
- 2x * -7 = -14x
-
Multiply -1 by each term in the second binomial:
- -1 * x² = -x²
- -1 * -3x = 3x
- -1 * -7 = 7
-
Combine the results:
- 2x³ - 6x² - 14x - x² + 3x + 7
-
Simplify by combining like terms:
- 2x³ - 7x² - 11x + 7
Conclusion
By applying the distributive property, we have successfully expanded the expression (2x - 1)(x² - 3x - 7) to 2x³ - 7x² - 11x + 7. This process is essential for simplifying algebraic expressions and solving equations.