(2x%5E2-9).jpeg "(3x^2+1)(2x^2-9)")
Expanding the Expression: (3x² + 1)(2x² - 9)
This article will guide you through the steps of expanding the expression (3x² + 1)(2x² - 9).
Understanding the Process
Expanding the given expression involves using the distributive property or FOIL method. Both methods allow us to multiply each term in the first binomial with each term in the second binomial.
Using the Distributive Property:
- Distribute the first term of the first binomial:
- 3x² * (2x² - 9) = 6x⁴ - 27x²
- Distribute the second term of the first binomial:
- 1 * (2x² - 9) = 2x² - 9
- Combine the results:
- (6x⁴ - 27x²) + (2x² - 9) = 6x⁴ - 25x² - 9
Using the FOIL Method:
FOIL stands for First, Outer, Inner, Last. This method outlines a specific order for multiplying the terms.
- First: 3x² * 2x² = 6x⁴
- Outer: 3x² * -9 = -27x²
- Inner: 1 * 2x² = 2x²
- Last: 1 * -9 = -9
- Combine: 6x⁴ - 27x² + 2x² - 9 = 6x⁴ - 25x² - 9
Conclusion:
Both methods lead to the same expanded expression: 6x⁴ - 25x² - 9. Expanding expressions is crucial for simplifying equations, solving problems in algebra, and performing various operations in mathematics.