(2a%2B3).jpeg "(2a-5)(2a+3)")
Expanding the Expression: (2a-5)(2a+3)
This article will guide you through the process of expanding the given expression: (2a-5)(2a+3).
Understanding the Expression
The expression (2a-5)(2a+3) represents the product of two binomials. Binomials are algebraic expressions with two terms. In this case:
- (2a-5): This binomial has the terms 2a and -5.
- (2a+3): This binomial has the terms 2a and 3.
Expanding using the FOIL method
The most common method for expanding binomials is the FOIL method. FOIL stands for:
- F: First terms of each binomial.
- O: Outer terms of each binomial.
- I: Inner terms of each binomial.
- L: Last terms of each binomial.
Following this method, we expand the expression:
- F: (2a)(2a) = 4a²
- O: (2a)(3) = 6a
- I: (-5)(2a) = -10a
- L: (-5)(3) = -15
Combining like terms
After applying the FOIL method, we obtain:
4a² + 6a - 10a - 15
Combining the like terms (6a and -10a), we get the final expanded expression:
4a² - 4a - 15
Conclusion
Therefore, the expanded form of the expression (2a-5)(2a+3) is 4a² - 4a - 15. By applying the FOIL method, we can effectively multiply binomials and simplify the resulting expressions.